<\/span>Nh\u1eefng ki\u1ebfn th\u1ee9c c\u1ea7n nh\u1edb v\u1ec1 s\u1ed1 th\u1ef1c<\/b><\/span><\/span><\/h2>\n

<\/span>S\u1ed1 th\u1ef1c l\u00e0 g\u00ec?<\/b><\/span><\/span><\/h3>\n

Theo Wikipedia th\u00ec m\u1ed9t\u00a0s\u1ed1 th\u1ef1c bao g\u1ed3m t\u1ea5t c\u1ea3 c\u00e1c\u00a0s\u1ed1 h\u1eefu t\u1ec9, ch\u1eb3ng h\u1ea1n nh\u01b0\u00a0s\u1ed1 nguy\u00ean\u00a0\u22125 v\u00e0\u00a0ph\u1ea7n s\u1ed1\u00a04\/3 v\u00e0 t\u1ea5t c\u1ea3 c\u00e1c\u00a0s\u1ed1 v\u00f4 t\u1ec9, ch\u1eb3ng h\u1ea1n nh\u01b0 \u221a 2 (1.41421356…,\u00a0c\u0103n b\u1eadc hai c\u1ee7a 2,\u00a0s\u1ed1 \u0111\u1ea1i s\u1ed1\u00a0v\u00f4 t\u1ec9).\u00a0<\/span><\/p>\n

<\/span><\/p>\n

Ho\u1eb7c m\u1ed9t c\u00e1ch d\u1ec5 hi\u1ec3u h\u01a1n l\u00e0 s\u1ed1 th\u00edch ch\u00ednh l\u00e0 t\u1eadp h\u1ee3p bao g\u1ed3m s\u1ed1 d\u01b0\u01a1ng (nh\u01b0 1, 2, 3), s\u1ed1 0, s\u1ed1 \u00e2m (-1,- 2, -3), s\u1ed1 h\u1eefu t\u1ec9, s\u1ed1 v\u00f4 t\u1ec9. T\u1ee9c c\u00f3 ngh\u0129a s\u1ed1 th\u1ef1c g\u1ed3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c xem l\u00e0 c\u00e1c \u0111i\u1ec3m n\u1eb1m tr\u00ean tr\u1ee5c s\u1ed1 d\u00e0i v\u00f4 h\u1ea1n.\u00a0 Ng\u1eafn g\u1ecdn h\u01a1n th\u00ec s\u1ed1 th\u1ef1c l\u00e0 t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9.<\/span><\/p>\n

<\/span>T\u00ednh ch\u1ea5t c\u1ee7a s\u1ed1 th\u1ee9c<\/b><\/span><\/span><\/h3>\n

\n
• B\u1ea5t k\u1ef3\u00a0s\u1ed1\u00a0th\u1ef1c\u00a0kh\u00e1c kh\u00f4ng\u00a0l\u00e0\u00a0s\u1ed1 \u00e2m\u00a0ho\u1eb7c\u00a0s\u1ed1 d\u01b0\u01a1ng.<\/span><\/li>\n
• T\u1ed5ng hay t\u00edch c\u1ee7a hai s\u1ed1 th\u1ef1c kh\u00f4ng \u00e2m l\u00e0 m\u1ed9t s\u1ed1 th\u1ef1c kh\u00f4ng \u00e2m.<\/span><\/li>\n
• S\u1ed1 th\u1ef1c l\u00e0 t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n c\u00e1c s\u1ed1 v\u00f4 c\u00f9ng nhi\u1ec1u kh\u00f4ng \u0111\u1ebfm \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 th\u1ef1c.<\/span><\/li>\n
• C\u00f3 h\u1ec7 th\u1ed1ng c\u00e1c t\u1eadp h\u1ee3p con v\u00f4 h\u1ea1n c\u00f3 th\u1ec3 \u0111\u1ebfm \u0111\u01b0\u1ee3c c\u1ee7a c\u00e1c s\u1ed1 th\u1ef1c.<\/span><\/li>\n
• S\u1ed1 th\u1ef1c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 th\u1ec3 hi\u1ec7n\u00a0c\u00e1c ph\u00e9p \u0111o\u00a0\u0111\u1ea1i l\u01b0\u1ee3ng\u00a0li\u00ean t\u1ee5c<\/span><\/li>\n
• S\u1ed1 th\u1ef1c c\u00f3 th\u1ec3 bi\u1ec3u th\u1ecb b\u1eb1ng bi\u1ec3u di\u1ec5n th\u1eadp ph\u00e2n.<\/span><\/li>\n<\/ul>\n

  <\/span>\u0110\u1ecbnh ngh\u0129a v\u1ec1 t\u1eadp h\u1ee3p R<\/b><\/span><\/span><\/h2>\n

  <\/span>R l\u00e0 g\u00ec?\u00a0<\/b><\/span><\/span><\/h3>\n

  R trong to\u00e1n h\u1ecdc l\u00e0 g\u00ec? C\u00e2u tr\u1ea3 l\u1eddi: R ch\u00ednh l\u00e0 k\u00ed hi\u1ec7u c\u1ee7a s\u1ed1 th\u1ef1c bao g\u1ed3m s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9.\u00a0<\/span><\/p>\n

  Ta c\u00f3: T\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c k\u00ed hi\u1ec7u l\u00e0 R (<\/span>R=Q<\/b> U <\/span>I<\/b>)\u00a0<\/span><\/span><\/p>\n

  T\u1eadp h\u1ee3p c\u1ee7a c\u00e1c s\u1ed1 th\u1ef1c \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n qua h\u00ecnh v\u1ebd sau \u0111\u00e2y:<\/span>\u00a0<\/span><\/span><\/p>\n

  Trong \u0111\u00f3:<\/span><\/p>\n

  N: T\u1eadp h\u1ee3p s\u1ed1 t\u1ef1 nhi\u00ean<\/span><\/p>\n

  Z: T\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean<\/span><\/p>\n

  Q: T\u1eadp h\u1ee3p s\u1ed1 h\u1eefu t\u1ec9<\/span><\/p>\n

  I = RQ: T\u1eadp h\u1ee3p s\u1ed1 v\u00f4 t\u1ec9<\/span><\/p>\n

  V\u1eady R l\u00e0 t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c<\/span><\/p>\n

  <\/span>Tr\u1ee5c s\u1ed1 th\u1ef1c<\/b><\/span><\/span><\/h3>\n

  M\u1ed1i s\u1ed1 th\u1ef1c \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi m\u1ed9t \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1. V\u00e0 ng\u01b0\u1ee3c l\u1ea1i, t\u1ee9c m\u1ed7i \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1 s\u1ebd bi\u1ec3u di\u1ec5n m\u1ed9t s\u1ed1 th\u1ef1c. Ch\u1ec9 c\u00f3 t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c m\u1edbi c\u00f3 th\u1ec3 l\u1ea5p \u0111\u1ea7y tr\u1ee5c s\u1ed1.\u00a0<\/span><\/p>\n

  <\/span><\/p>\n

  Trong <\/span>t\u1eadp h\u1ee3p R, ta c\u0169ng \u0111\u1ecbnh ngh\u0129a c\u00e1c ph\u00e9p to\u00e1n c\u1ed9ng tr\u1eeb, nh\u00e2n, chia, l\u0169y th\u1eeba, c\u0103n b\u1eadc…V\u00e0 trong c\u00e1c ph\u00e9p to\u00e1n c\u00e1c s\u1ed1 th\u1ef1c c\u0169ng c\u00f3 c\u00e1c t\u00ednh ch\u1ea5t nh\u01b0 c\u00e1c ph\u00e9p to\u00e1n trong t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9.\u00a0<\/span><\/span><\/p>\n

  Ta c\u00f3: N <\/span>\u2282<\/span>\u00a0Z <\/span>\u2282<\/span>\u00a0Q <\/span>\u2282<\/span>\u00a0R.<\/span><\/span><\/p>\n

  <\/span>C\u00e1c thu\u1ed9c t\u00ednh c\u1ee7a s\u1ed1 th\u1ef1c\u00a0<\/b><\/span><\/span><\/h3>\n

  K\u00fd hi\u1ec7u R trong to\u00e1n h\u1ecdc \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 s\u1ed1 th\u1ef1c v\u00e0 ch\u00fang c\u00f3 c\u00e1c thu\u1ed9c t\u00ednh l\u00e0:<\/span><\/p>\n

  \n
  • Ch\u00fang cho bi\u1ebft c\u00e1c s\u1ed1 th\u1ef1c bao g\u1ed3m m\u1ed9t tr\u01b0\u1eddng, v\u1edbi ph\u00e9p c\u1ed9ng v\u00e0 ph\u00e9p nh\u00e2n c\u00f9ng v\u1edbi ph\u00e9p chia cho c\u00e1c s\u1ed1 kh\u00e1c 0. Ch\u00fang c\u00f3 th\u1ec3 s\u1eafp x\u1ebfp tr\u00ean m\u1ed9t tr\u1ee5c s\u1ed1 ho\u00e0nh theo c\u00e1ch t\u01b0\u01a1ng th\u00edch v\u1edbi ph\u00e9p c\u1ed9ng v\u00e0 ph\u00e9p nh\u00e2n.<\/span><\/li>\n
  • Ch\u00fang cho bi\u1ebft n\u1ebfu t\u1eadp h\u1ee3p m\u1ed9t s\u1ed1 th\u1ef1c kh\u00f4ng tr\u1ed1ng c\u00f3 gi\u1edbi h\u1ea1n tr\u00ean\u00a0 th\u00ec n\u00f3 c\u00f3 c\u1eadn tr\u00ean ch\u00ednh l\u00e0 nh\u1eefng s\u1ed1 th\u1ef1c nh\u1ecf nh\u1ea5t.\u00a0<\/span><\/li>\n<\/ul>\n

    <\/span>V\u00ed d\u1ee5 d\u1ec5 hi\u1ec3u v\u1ec1 s\u1ed1 th\u1ef1c trong to\u00e1n h\u1ecdc<\/b><\/span><\/span><\/h3>\n

    T\u1eadp h\u1ee3p\u00a0R\u00a0l\u00e0 k\u00fd hi\u1ec7u c\u1ee7a t\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c, g\u1ed3m s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9:<\/span><\/p>\n

    Ch\u1eb3ng h\u1ea1n nh\u01b0\u00a0s\u1ed1 nguy\u00ean l\u00e0:\u00a0\u22125, 2, 3, -8…<\/span><\/p>\n

    Ph\u00e2n S\u1ed1 l\u00e0:\u00a04\/3, 8\/5,..<\/span><\/p>\n

    S\u1ed1 V\u00f4 T\u1ef7 nh\u01b0: \u221a 2 (1.41421356…); 3,1456;…<\/span><\/p>\n

    Nhi\u1ec1u ng\u01b0\u1eddi th\u1eafc m\u1eafc v\u1ec1 0 c\u00f3 ph\u1ea3i l\u00e0 s\u1ed1 nguy\u00ean kh\u00f4ng? C\u00e2u tr\u1ea3 l\u1eddi l\u00e0 c\u00f3, b\u1edfi s\u1ed1 nguy\u00ean l\u00e0\u00a0t\u1eadp h\u1ee3p bao g\u1ed3m c\u00e1c s\u1ed1 kh\u00f4ng (0), s\u1ed1 t\u1ef1 nhi\u00ean d\u01b0\u01a1ng v\u00e0 c\u00e1c s\u1ed1 \u0111\u1ed1i c\u1ee7a ch\u00fang c\u00f2n g\u1ecdi l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean \u00e2m. T\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean l\u00e0 v\u00f4 h\u1ea1n nh\u01b0ng c\u00f3 th\u1ec3 \u0111\u1ebfm \u0111\u01b0\u1ee3c v\u00e0 k\u00ed hi\u1ec7u l\u00e0 Z.<\/span><\/p>\n

    K\u1ebft lu\u1eadn<\/b><\/span><\/p>\n

    V\u1eady khi m\u1ed9t ai \u0111\u00f3 h\u1ecfi b\u1ea1n s\u1ed1 th\u1ef1c l\u00e0 g\u00ec, R l\u00e0 g\u00ec hay R l\u00e0 t\u1eadp h\u1ee3p s\u1ed1 g\u00ec? Th\u00ec v\u1edbi nh\u1eefng ki\u1ebfn th\u1ee9c trong b\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u00fap b\u1ea1n tr\u1ea3 l\u1eddi ch\u00ednh x\u00e1c c\u00e1c c\u00e2u h\u1ecfi \u0111\u00f3. Hi v\u1ecdng c\u00e1c b\u1ea1n s\u1ebd n\u1eafm r\u00f5 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 t\u1eadp h\u1ee3p r l\u00e0 g\u00ec trong to\u00e1n h\u1ecdc \u0111\u1ec3 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp \u0111\u01b0\u1ee3c nhanh g\u1ecdn v\u00e0 d\u1ec5 d\u00e0ng h\u01a1n.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

    Trong b\u00e0i vi\u1ebft n\u00e0y ch\u00fang t\u00f4i s\u1ebd c\u00f9ng c\u00e1c b\u1ea1n t\u00ecm hi\u1ec3u v\u1ec1 s\u1ed1 th\u1ef1c l\u00e0 g\u00ec. Nh\u1eefng kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n v\u1ec1 s\u1ed1 th\u1ef1c, c\u00e1c t\u00ednh ch\u1ea5t c\u0169ng nh\u01b0 nh\u1eefng v\u00ed d\u1ee5 minh h\u1ecda \u0111\u1ec3 c\u00e1c b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n vai tr\u00f2 c\u1ee7a s\u1ed1 th\u1ef1c trong To\u00e1n h\u1ecdc nh\u01b0 th\u1ebf n\u00e0o.\u00a0 Nh\u1eefng ki\u1ebfn th\u1ee9c […]<\/p>\n","protected":false},"author":1,"featured_media":359,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"_links":{"self":[{"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/posts\/357"}],"collection":[{"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/comments?post=357"}],"version-history":[{"count":3,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/posts\/357\/revisions"}],"predecessor-version":[{"id":583,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/posts\/357\/revisions\/583"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/media\/359"}],"wp:attachment":[{"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/media?parent=357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/categories?post=357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kienthuconline24h.com\/wp-json\/wp\/v2\/tags?post=357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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