Question

Find the square roots of following surds :
$5+2\sqrt{6}$.

Answer 1

$5+2\sqrt{6}=3+2+2\sqrt{6}$

$=3+2\sqrt{6}+2$

$=(\sqrt{3}{)}^2+2\sqrt{3\times 2}+(\sqrt{2}{)}^2=(\sqrt{3}+\sqrt{2}{)}^2$.

$\therefore \sqrt{5+2\sqrt{6}}=\pm \sqrt{(3+\sqrt{2}{)}^2}=\pm (\sqrt{3}+\sqrt{2})$ , which is the required solution.