Question

Find the square root of
$16-2\sqrt{20}-2\sqrt{28}+2\sqrt{35}$

Answer 1

$16-2\sqrt{20}-2\sqrt{28}+2\sqrt{35}$

$=16+2\times (-2)\times \sqrt{5}+2\times (-2)\times \sqrt{7}+2\sqrt{5}\times \sqrt{7}$

$=(-2{)}^2+5+7+2\times (-2)\times \sqrt{5}+2\times (-2)\times \sqrt{7}+2\sqrt{5}\times \sqrt{7}$

$=(-2+\sqrt{5}+\sqrt{7}{)}^2$

Hence, square root of $16-2\sqrt{20}-2\sqrt{28}+2\sqrt{35}$ is $\pm (-2+\sqrt{5}+\sqrt{7})$