Question

The square root of $14+6\sqrt{5}$ is

Answer 1

given, $\sqrt{14+6\sqrt{5}}$

$=\sqrt{14+2\times 3\sqrt{5}}$

$=\sqrt{9+5+2\times 3\sqrt{5}}$

$=\sqrt{9+2\times 3\sqrt{5}+5}$

$=\sqrt{(3{)}^2+2\times 3\sqrt{5}+(\sqrt{5}{)}^2}$

$=\sqrt{(3+\sqrt{5}{)}^2}$

$=3+\sqrt{5}$