1. √7-4 √3 2. √21-8 √5 3. √28-10 √3 4. √3+ √8

1. √7-4 √3
2. √21-8 √5
3. √28-10 √3
4. √3+ √8

0 bình luận về “1. √7-4 √3 2. √21-8 √5 3. √28-10 √3 4. √3+ √8”

  1. 1)

    `\sqrt{7-4\sqrt3}`

    `=\sqrt{7-2.2\sqrt3}`

    `=\sqrt{4-2.2.\sqrt3+3}`

    `=\sqrt{2^2-2.2.\sqrt3+(\sqrt3)^2}`

    `=\sqrt{(2-\sqrt3)^2}`

    `=|2-\sqrt3|`  

    `=2-\sqrt3`   (Vì `2>\sqrt3`)

    2)

    `\sqrt{21-8\sqrt5}`

    `=\sqrt{16-2.4\sqrt5+5}`

    `=\sqrt{4^2-2.4\sqrt5+(\sqrt5)^2}`

    `=\sqrt{(4-\sqrt5)^2}`

    `=|4-\sqrt5|`

    `=4-\sqrt5`  (Vì `4>\sqrt5`)

    3)

    `\sqrt{28-10\sqrt3}`

    `=\sqrt{25-2.5\sqrt3+3}`

    `=\sqrt{5^2-2.5\sqrt3+(\sqrt3)^2}`

    `=\sqrt{(5-\sqrt3)^2}`

    `=|5-\sqrt3|`

    `=5-\sqrt3`  (Vì `5>\sqrt3`)

    4)

    `\sqrt{3+\sqrt8}`

    `=\sqrt{2+2\sqrt2+1}`

    `=\sqrt{(\sqrt2)^2+2.1\sqrt2+1}`

    `=\sqrt{(\sqrt2+1)^2}`

    `=|\sqrt2+1|`

    `=\sqrt2+1`

     

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