Simplification via Denesting Radicals

Question

just wondering if you could help me out with a question, cheers.

Simplify/Generalize: $\sqrt{a+\sqrt b} \pm \sqrt{a-\sqrt b}$

Answer 1

$\sqrt{a+{\sqrt b}} ± \sqrt{a-{\sqrt b}} = t$

$t^2=a+\sqrt b +a-\sqrt b ± 2 \sqrt {a^2 -b}=2(a ± \sqrt {a^2-b})$

$t=± \sqrt {2(a ± \sqrt {a^2-b})}$

For a>0 and b>0, a must be greater than $\sqrt b$ and $\sqrt{a+{\sqrt b}} > \sqrt{a-{\sqrt b}} $, therefore t is positive that is:

$t= \sqrt {2(a ± \sqrt {a^2-b})}$