Question

Find the square root of following surds:
$2-\sqrt{3}$

Answer 1

Square root of the surd: $2-\sqrt{3}$

$\Rightarrow \sqrt{2-\sqrt{3}}$

$=\frac{1}{\sqrt{2}}\sqrt{4-2\sqrt{3}}$

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

$=\frac{1}{\sqrt{2}}\sqrt{(\sqrt{3}+1{)}^2}$

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