Question

Find the square root of
$6+\sqrt{12}-\sqrt{24}-\sqrt{8}$

Answer 1

$6+4\sqrt{12}-4\sqrt{24}-\sqrt{8}$

$=6+2\times \sqrt{3}\times 1+2\times (-\sqrt{2})\times \sqrt{3}+2\times 1\times (-\sqrt{2})$

$=1+2+3+2\times \sqrt{3}\times 1+2\times (-\sqrt{2})\times \sqrt{3}+2\times 1\times (-\sqrt{2})$

$=(1+\sqrt{3}-\sqrt{2}{)}^2$

Hence square root of $6+4\sqrt{12}-4\sqrt{24}-\sqrt{8}$ is $=\pm (1+\sqrt{3}-\sqrt{2})$