Question

Find the square root of following surds:
$8-3\sqrt{7}$

Answer 1

Square root of the surd

$\Rightarrow \sqrt{8-3\sqrt{7}}$

$=\frac{1}{\sqrt{2}}\sqrt{16-6\sqrt{7}}$

$=\frac{1}{\sqrt{2}}\sqrt{(\sqrt{7}{)}^2+3^2-2(3\left)\right(\sqrt{7})}$

$=\pm \frac{1}{\sqrt{2}}(\sqrt{7}-3)$.