Question

Find the square root of following surds:
$9+2\sqrt{14}$.

Answer 1

Square root of surd $9+2\sqrt{14}$:

$\Rightarrow \sqrt{9+2\sqrt{14}}$

$=\sqrt{9+2\sqrt{7}\sqrt{2}}$

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

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

$=\pm (\sqrt{7}+\sqrt{2})$, which is the required solution.