{"id":28206,"date":"2023-09-11T12:51:11","date_gmt":"2023-09-11T05:51:11","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi"},"modified":"2023-09-11T12:51:11","modified_gmt":"2023-09-11T05:51:11","slug":"r-la-gi","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi","title":{"rendered":"T\u00ecm hi\u1ec3u v\u1ec1 R trong to\u00e1n h\u1ecdc: T\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c v\u00e0 c\u00e1c thu\u1ed9c t\u00ednh"},"content":{"rendered":"<p>&#8220;R l\u00e0 g\u00ec? T\u00ecm hi\u1ec3u v\u1ec1 m\u1ed9t ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh \u0111a m\u1ee5c \u0111\u00edch, ph\u1ed5 bi\u1ebfn v\u00e0 m\u1ea1nh m\u1ebd. Kh\u00e1m ph\u00e1 c\u00e1c kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n v\u00e0 t\u00ednh n\u0103ng c\u1ee7a R, c\u00f9ng l\u1ee3i \u00edch c\u1ee7a vi\u1ec7c s\u1eed d\u1ee5ng n\u00f3 trong ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 th\u1ed1ng k\u00ea.&#8221;<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6ace433cc64ef\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6ace433cc64ef\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#1_R_la_tap_hop_so_gi\" title=\"1. R l\u00e0 t\u1eadp h\u1ee3p s\u1ed1 g\u00ec?\">1. R l\u00e0 t\u1eadp h\u1ee3p s\u1ed1 g\u00ec?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Tinh_chat_cua_tap_hop_R\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p R:\">T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p R:<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Vi_du\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#2_R_la_gi_trong_toan_hoc\" title=\"2. R l\u00e0 g\u00ec trong to\u00e1n h\u1ecdc?\">2. R l\u00e0 g\u00ec trong to\u00e1n h\u1ecdc?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Tinh_chat_cua_tap_hop_R-2\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p R:\">T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p R:<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Vi_du-2\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#3_R_la_ky_hieu_cua_tap_so_thuc_bao_gom_so_huu_ti_va_vo_ti\" title=\"3. R l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a t\u1eadp s\u1ed1 th\u1ef1c, bao g\u1ed3m s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 v\u00f4 t\u1ec9.\">3. R l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a t\u1eadp s\u1ed1 th\u1ef1c, bao g\u1ed3m s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 v\u00f4 t\u1ec9.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#31_So_huu_ti\" title=\"3.1 S\u1ed1 h\u1eefu t\u1ec9\">3.1 S\u1ed1 h\u1eefu t\u1ec9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#32_So_vo_ti\" title=\"3.2 S\u1ed1 v\u00f4 t\u1ec9\">3.2 S\u1ed1 v\u00f4 t\u1ec9<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Danh_sach_cac_loai_so_trong_tap_R\" title=\"Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:\">Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#4_R_la_tap_so_lon_nhat_tren_tap_so_tu_nhien_N_va_tap_so_nguyen_Z\" title=\"4. R l\u00e0 t\u1eadp s\u1ed1 l\u1edbn nh\u1ea5t tr\u00ean t\u1eadp s\u1ed1 t\u1ef1 nhi\u00ean N v\u00e0 t\u1eadp s\u1ed1 nguy\u00ean Z.\">4. R l\u00e0 t\u1eadp s\u1ed1 l\u1edbn nh\u1ea5t tr\u00ean t\u1eadp s\u1ed1 t\u1ef1 nhi\u00ean N v\u00e0 t\u1eadp s\u1ed1 nguy\u00ean Z.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Danh_sach_cac_loai_so_trong_tap_R-2\" title=\"Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:\">Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#5_So_thuc_la_tap_hop_bao_gom_so_duong_so_0_so_am_so_huu_ti_va_so_vo_ti\" title=\"5. S\u1ed1 th\u1ef1c l\u00e0 t\u1eadp h\u1ee3p bao g\u1ed3m s\u1ed1 d\u01b0\u01a1ng, s\u1ed1 0, s\u1ed1 \u00e2m, s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9.\">5. S\u1ed1 th\u1ef1c l\u00e0 t\u1eadp h\u1ee3p bao g\u1ed3m s\u1ed1 d\u01b0\u01a1ng, s\u1ed1 0, s\u1ed1 \u00e2m, s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#51_So_duong\" title=\"5.1 S\u1ed1 d\u01b0\u01a1ng\">5.1 S\u1ed1 d\u01b0\u01a1ng<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#52_So_am\" title=\"5.2 S\u1ed1 \u00e2m\">5.2 S\u1ed1 \u00e2m<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#53_So_0\" title=\"5.3 S\u1ed1 0\">5.3 S\u1ed1 0<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#Danh_sach_cac_loai_so_trong_tap_R-3\" title=\"Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:\">Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#6_Tinh_chat_cua_tap_hop_so_thuc_trong_toan_hoc\" title=\"6. T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc.\">6. T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#61_Dac_diem_chung_cua_so_thuc\" title=\"6.1. \u0110\u1eb7c \u0111i\u1ec3m chung c\u1ee7a s\u1ed1 th\u1ef1c\">6.1. \u0110\u1eb7c \u0111i\u1ec3m chung c\u1ee7a s\u1ed1 th\u1ef1c<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#611_Phep_toan_tren_so_thuc\" title=\"6.1.1. Ph\u00e9p to\u00e1n tr\u00ean s\u1ed1 th\u1ef1c\">6.1.1. Ph\u00e9p to\u00e1n tr\u00ean s\u1ed1 th\u1ef1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#612_Su_bieu_dien_cua_so_thuc\" title=\"6.1.2. S\u1ef1 bi\u1ec3u di\u1ec5n c\u1ee7a s\u1ed1 th\u1ef1c\">6.1.2. S\u1ef1 bi\u1ec3u di\u1ec5n c\u1ee7a s\u1ed1 th\u1ef1c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#62_Cac_tinh_chat_quan_trong_cua_so_thuc\" title=\"6.2. C\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng c\u1ee7a s\u1ed1 th\u1ef1c\">6.2. C\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng c\u1ee7a s\u1ed1 th\u1ef1c<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#621_Tinh_ket_hop\" title=\"6.2.1. T\u00ednh k\u1ebft h\u1ee3p\">6.2.1. T\u00ednh k\u1ebft h\u1ee3p<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#622_Tinh_giao_hoan\" title=\"6.2.2. T\u00ednh giao ho\u00e1n\">6.2.2. T\u00ednh giao ho\u00e1n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#623_Tinh_phan_phoi\" title=\"6.2.3. T\u00ednh ph\u00e2n ph\u1ed1i\">6.2.3. T\u00ednh ph\u00e2n ph\u1ed1i<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#624_Tinh_chia_het\" title=\"6.2.4. T\u00ednh chia h\u1ebft\">6.2.4. T\u00ednh chia h\u1ebft<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#7_Vi_du_ve_cac_so_thuc_trong_toan_hoc\" title=\"7. V\u00ed d\u1ee5 v\u1ec1 c\u00e1c s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc.\">7. V\u00ed d\u1ee5 v\u1ec1 c\u00e1c s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#71_So_Pi_%CF%80\" title=\"7.1. S\u1ed1 Pi (\u03c0)\">7.1. S\u1ed1 Pi (\u03c0)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#72_So_can_bac_hai_%E2%88%9A2\" title=\"7.2. S\u1ed1 c\u0103n b\u1eadc hai (\u221a2)\">7.2. S\u1ed1 c\u0103n b\u1eadc hai (\u221a2)<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#8_Bai_tap_lien_quan_den_so_thuc_va_cach_giai_quyet_chung\" title=\"8. B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 th\u1ef1c v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebft ch\u00fang.\">8. B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 th\u1ef1c v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebft ch\u00fang.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#81_Bai_tap_1_Tinh_tong_cua_hai_so_thuc\" title=\"8.1. B\u00e0i t\u1eadp 1: T\u00ednh t\u1ed5ng c\u1ee7a hai s\u1ed1 th\u1ef1c\">8.1. B\u00e0i t\u1eadp 1: T\u00ednh t\u1ed5ng c\u1ee7a hai s\u1ed1 th\u1ef1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#82_Bai_tap_2_Tim_gia_tri_lon_nhat_va_nho_nhat_trong_mot_day_so_thuc\" title=\"8.2. B\u00e0i t\u1eadp 2: T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t trong m\u1ed9t d\u00e3y s\u1ed1 th\u1ef1c\">8.2. B\u00e0i t\u1eadp 2: T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t trong m\u1ed9t d\u00e3y s\u1ed1 th\u1ef1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/r-la-gi\/#83_Bai_tap_3_Giai_phuong_trinh_so_thuc\" title=\"8.3. B\u00e0i t\u1eadp 3: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh s\u1ed1 th\u1ef1c\">8.3. B\u00e0i t\u1eadp 3: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh s\u1ed1 th\u1ef1c<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"1_R_la_tap_hop_so_gi\"><\/span>1. R l\u00e0 t\u1eadp h\u1ee3p s\u1ed1 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>T\u1eadp h\u1ee3p R trong to\u00e1n h\u1ecdc \u0111\u1ea1i di\u1ec7n cho t\u1eadp s\u1ed1 th\u1ef1c. N\u00f3 bao g\u1ed3m t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean tr\u1ee5c s\u1ed1, t\u1eeb c\u00e1c s\u1ed1 nguy\u00ean \u0111\u1ebfn c\u00e1c s\u1ed1 v\u00f4 t\u1ec9. T\u1eadp R l\u00e0 m\u1ed9t t\u1eadp con c\u1ee7a t\u1eadp s\u1ed1 ph\u1ee9c C v\u00e0 l\u00e0 m\u1edf r\u1ed9ng c\u1ee7a t\u1eadp s\u1ed1 h\u1eefu t\u1ec9 Q.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_tap_hop_R\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p R:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>T\u1eadp R l\u00e0 kh\u00f4ng gi\u1edbi h\u1ea1n, \u0111i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t trong t\u1eadp h\u1ee3p n\u00e0y.<\/li>\n<li>M\u1ed7i s\u1ed1 trong t\u1eadp R c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng m\u1ed9t d\u00e3y v\u00f4 h\u1ea1n c\u00e1c ch\u1eef s\u1ed1 sau d\u1ea5u th\u1eadp ph\u00e2n.<\/li>\n<li>C\u00e1c ph\u00e9p to\u00e1n c\u01a1 b\u1ea3n nh\u01b0 c\u1ed9ng, tr\u1eeb, nh\u00e2n v\u00e0 chia \u0111\u1ec1u \u00e1p d\u1ee5ng cho c\u00e1c s\u1ed1 trong t\u1eadp R.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Trong t\u1eadp R, ta c\u00f3 c\u00e1c s\u1ed1 nguy\u00ean nh\u01b0 -3, 0 v\u00e0 5; c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 nh\u01b0 1\/2 v\u00e0 -3\/4; v\u00e0 c\u00e1c s\u1ed1 v\u00f4 t\u1ec9 nh\u01b0 \u221a2 v\u00e0 \u03c0 (pi). T\u1ed5ng qu\u00e1t, m\u1ecdi con s\u1ed1 b\u1ea1n ngh\u0129 \u0111\u1ebfn c\u00f3 th\u1ec3 thu\u1ed9c v\u00e0o t\u1eadp R.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"2_R_la_gi_trong_toan_hoc\"><\/span>2. R l\u00e0 g\u00ec trong to\u00e1n h\u1ecdc?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Trong to\u00e1n h\u1ecdc, k\u00fd hi\u1ec7u R th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u di\u1ec5n t\u1eadp s\u1ed1 th\u1ef1c. T\u1eadp s\u1ed1 th\u1ef1c bao g\u1ed3m t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean tr\u1ee5c s\u1ed1, t\u1eeb c\u00e1c s\u1ed1 nguy\u00ean \u0111\u1ebfn c\u00e1c s\u1ed1 v\u00f4 t\u1ec9.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_tap_hop_R-2\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p R:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>T\u1eadp R l\u00e0 m\u1ed9t t\u1eadp kh\u00f4ng gi\u1edbi h\u1ea1n, kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t.<\/li>\n<li>M\u1ed7i s\u1ed1 trong t\u1eadp R c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng m\u1ed9t d\u00e3y v\u00f4 h\u1ea1n c\u00e1c ch\u1eef s\u1ed1 sau d\u1ea5u th\u1eadp ph\u00e2n.<\/li>\n<li>C\u00e1c ph\u00e9p to\u00e1n c\u01a1 b\u1ea3n nh\u01b0 c\u1ed9ng, tr\u1eeb, nh\u00e2n v\u00e0 chia \u0111\u1ec1u \u00e1p d\u1ee5ng cho c\u00e1c s\u1ed1 trong t\u1eadp R.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-2\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>V\u00ed d\u1ee5 v\u1ec1 c\u00e1c s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc bao g\u1ed3m: -5, 0, 3\/4, \u221a2 (c\u0103n b\u1eadc hai c\u1ee7a 2), \u03c0 (pi), v\u00e0 e (s\u1ed1 Euler).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"3_R_la_ky_hieu_cua_tap_so_thuc_bao_gom_so_huu_ti_va_vo_ti\"><\/span>3. R l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a t\u1eadp s\u1ed1 th\u1ef1c, bao g\u1ed3m s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 v\u00f4 t\u1ec9.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"31_So_huu_ti\"><\/span>3.1 S\u1ed1 h\u1eefu t\u1ec9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 nh\u1eefng s\u1ed1 c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1, trong \u0111\u00f3 t\u1eed v\u00e0 m\u1eabu c\u1ee7a ph\u00e2n s\u1ed1 \u0111\u1ec1u l\u00e0 c\u00e1c s\u1ed1 nguy\u00ean. V\u00ed d\u1ee5, 1\/2, -3\/4, 5\/6 \u0111\u1ec1u l\u00e0 c\u00e1c s\u1ed1 h\u1eefu t\u1ec9. T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 Q.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"32_So_vo_ti\"><\/span>3.2 S\u1ed1 v\u00f4 t\u1ec9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 nh\u1eefng s\u1ed1 kh\u00f4ng th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 v\u00e0 kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb ch\u00ednh x\u00e1c khi \u0111\u01b0\u1ee3c vi\u1ebft th\u00e0nh m\u1ed9t con s\u1ed1 h\u1eefu h\u1ea1n. V\u00ed d\u1ee5, c\u0103n b\u1eadc hai (\u221a2), pi (\u03c0) \u0111\u1ec1u l\u00e0 c\u00e1c s\u1ed1 v\u00f4 t\u1ec9. T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 v\u00f4 t\u1ec9 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 I.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Danh_sach_cac_loai_so_trong_tap_R\"><\/span>Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>S\u1ed1 nguy\u00ean: bao g\u1ed3m c\u1ea3 c\u00e1c s\u1ed1 \u00e2m v\u00e0 kh\u00f4ng \u00e2m.<\/li>\n<li>S\u1ed1 th\u1eadp ph\u00e2n: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 sau d\u1ea5u ch\u1ea5m th\u1eadp ph\u00e2n.<\/li>\n<li>S\u1ed1 ph\u1ee9c: bao g\u1ed3m c\u1ea3 ph\u1ea7n th\u1ef1c v\u00e0 ph\u1ea7n \u1ea3o.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"4_R_la_tap_so_lon_nhat_tren_tap_so_tu_nhien_N_va_tap_so_nguyen_Z\"><\/span>4. R l\u00e0 t\u1eadp s\u1ed1 l\u1edbn nh\u1ea5t tr\u00ean t\u1eadp s\u1ed1 t\u1ef1 nhi\u00ean N v\u00e0 t\u1eadp s\u1ed1 nguy\u00ean Z.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>T\u1eadp s\u1ed1 th\u1ef1c R bao g\u1ed3m c\u1ea3 t\u1eadp s\u1ed1 t\u1ef1 nhi\u00ean N v\u00e0 t\u1eadp s\u1ed1 nguy\u00ean Z. T\u1eadp s\u1ed1 t\u1ef1 nhi\u00ean N bao g\u1ed3m c\u00e1c s\u1ed1 kh\u00f4ng \u00e2m (0, 1, 2, 3,&#8230;) v\u00e0 t\u1eadp s\u1ed1 nguy\u00ean Z bao g\u1ed3m c\u1ea3 c\u00e1c s\u1ed1 \u00e2m (-3, -2, -1) v\u00e0 kh\u00f4ng \u00e2m (0, 1, 2,&#8230;). S\u1ed1 th\u1ef1c trong R c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng m\u1ed9t \u0111i\u1ec3m tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng s\u1ed1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Danh_sach_cac_loai_so_trong_tap_R-2\"><\/span>Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>S\u1ed1 t\u1ef1 nhi\u00ean: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 kh\u00f4ng \u00e2m.<\/li>\n<li>S\u1ed1 nguy\u00ean: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 \u00e2m v\u00e0 kh\u00f4ng \u00e2m.<\/li>\n<li>S\u1ed1 h\u1eefu t\u1ec9: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1.<\/li>\n<li>S\u1ed1 v\u00f4 t\u1ec9: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 kh\u00f4ng th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"5_So_thuc_la_tap_hop_bao_gom_so_duong_so_0_so_am_so_huu_ti_va_so_vo_ti\"><\/span>5. S\u1ed1 th\u1ef1c l\u00e0 t\u1eadp h\u1ee3p bao g\u1ed3m s\u1ed1 d\u01b0\u01a1ng, s\u1ed1 0, s\u1ed1 \u00e2m, s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>S\u1ed1 th\u1ef1c l\u00e0 t\u1eadp h\u1ee3p bao g\u1ed3m t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng s\u1ed1. T\u1eadp h\u1ee3p n\u00e0y bao g\u1ed3m c\u00e1c lo\u1ea1i s\u1ed1 nh\u01b0 sau:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"51_So_duong\"><\/span>5.1 S\u1ed1 d\u01b0\u01a1ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 d\u01b0\u01a1ng l\u00e0 nh\u1eefng s\u1ed1 l\u1edbn h\u01a1n 0. V\u00ed d\u1ee5, 1, 2, 3 \u0111\u1ec1u l\u00e0 c\u00e1c s\u1ed1 d\u01b0\u01a1ng.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"52_So_am\"><\/span>5.2 S\u1ed1 \u00e2m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 \u00e2m l\u00e0 nh\u1eefng s\u1ed1 nh\u1ecf h\u01a1n 0. V\u00ed d\u1ee5, -1, -2, -3 \u0111\u1ec1u l\u00e0 c\u00e1c s\u1ed1 \u00e2m.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"53_So_0\"><\/span>5.3 S\u1ed1 0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 0 kh\u00f4ng thu\u1ed9c v\u00e0o b\u1ea5t k\u1ef3 lo\u1ea1i n\u00e0o kh\u00e1c trong t\u1eadp s\u1ed1 th\u1ef1c.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Danh_sach_cac_loai_so_trong_tap_R-3\"><\/span>Danh s\u00e1ch c\u00e1c lo\u1ea1i s\u1ed1 trong t\u1eadp R:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>S\u1ed1 d\u01b0\u01a1ng: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 l\u1edbn h\u01a1n 0.<\/li>\n<li>S\u1ed1 \u00e2m: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 nh\u1ecf h\u01a1n 0.<\/li>\n<li>S\u1ed1 nguy\u00ean: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 \u00e2m, kh\u00f4ng \u00e2m v\u00e0 0.<\/li>\n<li>S\u1ed1 h\u1eefu t\u1ec9: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1.<\/li>\n<li>S\u1ed1 v\u00f4 t\u1ec9: bao g\u1ed3m c\u1ea3 c\u00e1c con s\u1ed1 kh\u00f4ng th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"6_Tinh_chat_cua_tap_hop_so_thuc_trong_toan_hoc\"><\/span>6. T\u00ednh ch\u1ea5t c\u1ee7a t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"61_Dac_diem_chung_cua_so_thuc\"><\/span>6.1. \u0110\u1eb7c \u0111i\u1ec3m chung c\u1ee7a s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 th\u1ef1c l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p l\u1edbn v\u00e0 \u0111a d\u1ea1ng trong to\u00e1n h\u1ecdc, bao g\u1ed3m c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean, s\u1ed1 th\u1eadp ph\u00e2n v\u00e0 c\u00e1c s\u1ed1 v\u00f4 t\u1ec9. M\u1ed9t trong nh\u1eefng \u0111\u1eb7c \u0111i\u1ec3m chung c\u1ee7a t\u1eadp h\u1ee3p n\u00e0y l\u00e0 t\u00ednh li\u00ean t\u1ee5c, t\u1ee9c l\u00e0 kh\u00f4ng c\u00f3 kho\u1ea3ng c\u00e1ch r\u00f5 r\u00e0ng gi\u1eefa c\u00e1c s\u1ed1 th\u1ef1c. \u0110i\u1ec1u n\u00e0y cho ph\u00e9p ta di\u1ec5n t\u1ea3 v\u00e0 x\u1eed l\u00fd c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan \u0111\u1ebfn kh\u00f4ng gian v\u00e0 th\u1eddi gian m\u1ed9t c\u00e1ch linh ho\u1ea1t.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"611_Phep_toan_tren_so_thuc\"><\/span>6.1.1. Ph\u00e9p to\u00e1n tr\u00ean s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Trong t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c, ta c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p to\u00e1n c\u1ed9ng, tr\u1eeb, nh\u00e2n v\u00e0 chia gi\u1ed1ng nh\u01b0 trong c\u00e1c t\u1eadp h\u1ee3p con kh\u00e1c nh\u01b0 s\u1ed1 nguy\u00ean hay s\u1ed1 t\u1ef1 nhi\u00ean. Ngo\u00e0i ra, ta c\u0169ng c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng c\u00e1c ph\u00e9p to\u00e1n kh\u00e1c nh\u01b0 c\u0103n b\u1eadc hai, l\u0169y th\u1eeba v\u00e0 logarit.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"612_Su_bieu_dien_cua_so_thuc\"><\/span>6.1.2. S\u1ef1 bi\u1ec3u di\u1ec5n c\u1ee7a s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>S\u1ed1 th\u1ef1c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng s\u1ed1 g\u1ecdi l\u00e0 tr\u1ee5c s\u1ed1. M\u1ed7i \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1 t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t gi\u00e1 tr\u1ecb s\u1ed1 th\u1ef1c. \u0110i\u1ec1u n\u00e0y cho ph\u00e9p ta bi\u1ec3u di\u1ec5n v\u00e0 so s\u00e1nh c\u00e1c s\u1ed1 th\u1ef1c d\u1ec5 d\u00e0ng h\u01a1n.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"62_Cac_tinh_chat_quan_trong_cua_so_thuc\"><\/span>6.2. C\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng c\u1ee7a s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>C\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng c\u1ee7a t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c bao g\u1ed3m t\u00ednh k\u1ebft h\u1ee3p, t\u00ednh giao ho\u00e1n, t\u00ednh ph\u00e2n ph\u1ed1i v\u00e0 t\u00ednh chia h\u1ebft.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"621_Tinh_ket_hop\"><\/span>6.2.1. T\u00ednh k\u1ebft h\u1ee3p<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>T\u00ednh k\u1ebft h\u1ee3p cho ph\u00e9p ta thay \u0111\u1ed5i th\u1ee9 t\u1ef1 c\u00e1c ph\u00e9p to\u00e1n trong m\u1ed9t bi\u1ec3u th\u1ee9c s\u1ed1 h\u1ecdc m\u00e0 kh\u00f4ng l\u00e0m thay \u0111\u1ed5i k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"622_Tinh_giao_hoan\"><\/span>6.2.2. T\u00ednh giao ho\u00e1n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>T\u00ednh giao ho\u00e1n cho ph\u00e9p ta thay \u0111\u1ed5i v\u1ecb tr\u00ed c\u1ee7a hai th\u00e0nh ph\u1ea7n trong m\u1ed9t ph\u00e9p to\u00e1n m\u00e0 kh\u00f4ng l\u00e0m thay \u0111\u1ed5i k\u1ebft qu\u1ea3 cu\u1ed1i c\u00f9ng.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"623_Tinh_phan_phoi\"><\/span>6.2.3. T\u00ednh ph\u00e2n ph\u1ed1i<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>T\u00ednh ph\u00e2n ph\u1ed1i cho ph\u00e9p ta \u00e1p d\u1ee5ng c\u00e1c ph\u00e9p to\u00e1n nh\u00e2n v\u00e0 c\u1ed9ng l\u00ean c\u00e1c bi\u1ec3u th\u1ee9c c\u00f3 nhi\u1ec1u th\u00e0nh ph\u1ea7n.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"624_Tinh_chia_het\"><\/span>6.2.4. T\u00ednh chia h\u1ebft<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>T\u00ednh chia h\u1ebft cho ph\u00e9p ta chia m\u1ed9t s\u1ed1 th\u1ef1c cho m\u1ed9t s\u1ed1 kh\u00e1c m\u00e0 kh\u00f4ng g\u00e2y ra d\u01b0 th\u1eeba.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"7_Vi_du_ve_cac_so_thuc_trong_toan_hoc\"><\/span>7. V\u00ed d\u1ee5 v\u1ec1 c\u00e1c s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"71_So_Pi_%CF%80\"><\/span>7.1. S\u1ed1 Pi (\u03c0)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 Pi l\u00e0 m\u1ed9t v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh v\u1ec1 s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc. N\u00f3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng k\u00fd hi\u1ec7u \u03c0 v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 3.14159. S\u1ed1 Pi l\u00e0 t\u1ef7 l\u1ec7 gi\u1eefa chu vi c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a n\u00f3, v\u00e0 n\u00f3 xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn h\u00ecnh h\u1ecdc v\u00e0 t\u00ednh to\u00e1n.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"72_So_can_bac_hai_%E2%88%9A2\"><\/span>7.2. S\u1ed1 c\u0103n b\u1eadc hai (\u221a2)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 c\u0103n b\u1eadc hai (\u221a2) c\u0169ng l\u00e0 m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc. N\u00f3 kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean hay s\u1ed1 t\u1ef1 nhi\u00ean, v\u00e0 kh\u00f4ng th\u1ec3 bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 \u0111\u01a1n gi\u1ea3n. Gi\u00e1 tr\u1ecb c\u1ee7a c\u0103n b\u1eadc hai x\u1ea5p x\u1ec9 1.41421 v\u00e0 n\u00f3 xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111o l\u01b0\u1eddng, t\u00ednh to\u00e1n kho\u1ea3ng c\u00e1ch v\u00e0 t\u1ec9 l\u1ec7.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"8_Bai_tap_lien_quan_den_so_thuc_va_cach_giai_quyet_chung\"><\/span>8. B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 th\u1ef1c v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebft ch\u00fang.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"8. B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 th\u1ef1c v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebft ch\u00fang.\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/tim_hieu_ve_r_trong_toan_hoc_tap_hop_so_thuc_va_cac_thuoc_tinh.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"8. B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 th\u1ef1c v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebft ch\u00fang.\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"81_Bai_tap_1_Tinh_tong_cua_hai_so_thuc\"><\/span>8.1. B\u00e0i t\u1eadp 1: T\u00ednh t\u1ed5ng c\u1ee7a hai s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Cho hai s\u1ed1 th\u1ef1c a v\u00e0 b, t\u00ednh t\u1ed5ng c\u1ee7a ch\u00fang b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng ph\u00e9p to\u00e1n c\u1ed9ng.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"82_Bai_tap_2_Tim_gia_tri_lon_nhat_va_nho_nhat_trong_mot_day_so_thuc\"><\/span>8.2. B\u00e0i t\u1eadp 2: T\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t trong m\u1ed9t d\u00e3y s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Cho m\u1ed9t d\u00e3y s\u1ed1 th\u1ef1c, t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t v\u00e0 nh\u1ecf nh\u1ea5t trong d\u00e3y \u0111\u00f3 b\u1eb1ng c\u00e1ch so s\u00e1nh c\u00e1c s\u1ed1 v\u1edbi nhau.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"83_Bai_tap_3_Giai_phuong_trinh_so_thuc\"><\/span>8.3. B\u00e0i t\u1eadp 3: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh s\u1ed1 th\u1ef1c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Cho m\u1ed9t ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 bi\u1ebfn l\u00e0 m\u1ed9t s\u1ed1 th\u1ef1c, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00f3 \u0111\u1ec3 t\u00ecm ra gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn.<\/p>\n<p>Danh s\u00e1ch n\u00e0y ch\u1ec9 l\u00e0 m\u1ed9t v\u00ed d\u1ee5 v\u1ec1 c\u00e1c b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn s\u1ed1 th\u1ef1c v\u00e0 c\u00e1ch gi\u1ea3i quy\u1ebft ch\u00fang trong to\u00e1n h\u1ecdc. C\u00f2n r\u1ea5t nhi\u1ec1u lo\u1ea1i b\u00e0i t\u1eadp kh\u00e1c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u1ef9 n\u0103ng l\u00e0m vi\u1ec7c v\u1edbi s\u1ed1 th\u1ef1c v\u00e0 \u00e1p d\u1ee5ng c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a ch\u00fang v\u00e0o c\u00e1c v\u1ea5n \u0111\u1ec1 kh\u00e1c nhau.<\/p>\n<p>Tr\u00ean th\u1ef1c t\u1ebf, &#8220;r&#8221; l\u00e0 m\u1ed9t t\u1eeb vi\u1ebft t\u1eaft th\u00f4ng d\u1ee5ng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong nhi\u1ec1u ng\u1eef c\u1ea3nh kh\u00e1c nhau. Tuy nhi\u00ean, khi \u0111\u1ec1 c\u1eadp \u0111\u1ebfn c\u00e1c thu\u1eadt ng\u1eef c\u00f4ng ngh\u1ec7 th\u00f4ng tin, &#8220;r&#8221; th\u01b0\u1eddng l\u00e0 vi\u1ebft t\u1eaft c\u1ee7a ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh R, m\u1ed9t c\u00f4ng c\u1ee5 ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 th\u1ed1ng k\u00ea m\u1ea1nh m\u1ebd.<br \/>\n<iframe loading=\"lazy\" title=\"\u0110\u1ea1i s\u1ed1 10-T\u1eadp h\u1ee3p-c\u00e1c t\u1eadp h\u1ee3p s\u1ed1\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/8Tze-sxt2gw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;R l\u00e0 g\u00ec? T\u00ecm hi\u1ec3u v\u1ec1 m\u1ed9t ng\u00f4n ng\u1eef l\u1eadp tr\u00ecnh \u0111a m\u1ee5c \u0111\u00edch, ph\u1ed5 bi\u1ebfn v\u00e0 m\u1ea1nh m\u1ebd. Kh\u00e1m ph\u00e1 c\u00e1c kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n v\u00e0&#8230; <\/p>\n","protected":false},"author":1,"featured_media":28205,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-28206","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-khai-niem-1"],"_links":{"self":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/28206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/comments?post=28206"}],"version-history":[{"count":0,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/28206\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media\/28205"}],"wp:attachment":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media?parent=28206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/categories?post=28206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/tags?post=28206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}