$\sqrt{16+2\sqrt{63} }$ - $\sqrt{16-6\sqrt{7} }$

$\sqrt{16+2\sqrt{63}}-\sqrt{16-6\sqrt{7}}$

$=\sqrt{16+2\sqrt{9.7}}-\sqrt{16-6\sqrt{7}}$

$=\sqrt{16+2.3\sqrt{7}}-\sqrt{16-6\sqrt{7}}$

$=\sqrt{9+7+2.3.\sqrt{7}}-\sqrt{9+7-2.3\sqrt{7}}$

$=\sqrt{(9+\sqrt{7})^2}-\sqrt{(9-\sqrt{7})^2}$

$=\sqrt{(3+\sqrt{7})^2}-\sqrt{(3-\sqrt{7})^2}$

$=\left|3+\sqrt{7}\right|-\left|3-\sqrt{7}\right|$

$=3+\sqrt{7}-3+\sqrt{7}$

$=2\sqrt{7}$

Đáp án:

`=2\sqrt{7}`

Giải thích các bước giải:

`\sqrt{16+2\sqrt{63}}-\sqrt{16-6\sqrt{7}}`

`=\sqrt{(\sqrt{9})^2 -2.\sqrt{9}.\sqrt{7}+(\sqrt{7})^2}-\sqrt{(\sqrt{9})^2 -2.3.\sqrt{7}+(\sqrt{7})^2}`

`=\sqrt{3^2+2.3.\sqrt{7}+(\sqrt{7})^2} - \sqrt{3^2+2.3.\sqrt{7}+(\sqrt{7})^2}`

`=\sqrt{(3+\sqrt{7})^2} - \sqrt{(3-\sqrt{7})^2}`

`=|3+\sqrt{7}|-|3-\sqrt{7}|`

`=3+\sqrt{7}-3+\sqrt{7}`

`=2\sqrt{7}`

Vậy `\sqrt{16+2\sqrt{63}}-\sqrt{16-6\sqrt{7}}=2\sqrt{7}`