Question

Find the square root of following surds:
$a+\sqrt{a^2-b^2}$

Answer 1

Square root of Sure: $a+\sqrt{a^2-b^2}$

$\Rightarrow \sqrt{a+\sqrt{a^2-b^2}}$

$=\frac{1}{\sqrt{2}}\sqrt{2a+2\sqrt{a+b}\sqrt{a-b}}$

$=\frac{1}{\sqrt{2}}\sqrt{(\sqrt{a+b}+\sqrt{a-b})}$

$=\pm \frac{1}{\sqrt{2}}(\sqrt{a+b}+\sqrt{a-b})$.