Question

Find the square root of $2a+2\sqrt{a^2+b^2}$.

Answer 1

Now,

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

$=\left\{\right(a+ib)+(a-ib\left)\right\}+2\sqrt{(a+ib)(a-ib)}$ [ Where $i^2=-1$]

$=\{{\left(\sqrt{(a+ib)}\right)}^2+{\left(\sqrt{(a-ib)}\right)}^2\}+2\sqrt{(a+ib)(a-ib)}$

$=(\sqrt{a+ib}+\sqrt{a-ib}{)}^2$

Now, square root of the given number is $\pm (\sqrt{a+ib}+\sqrt{a-ib})$.