Question 21
Let $a$ and $b$ be positive integers with $a \gt b$. Suppose that
$$
\sqrt{\sqrt{a} + \sqrt{b}} + \sqrt{\sqrt{a} - \sqrt{b}}
$$
is an integer.
a. Must $\sqrt{a}$ be an integer?
b. Must $\sqrt{b}$ be an integer?
$$
\sqrt{\sqrt{a} + \sqrt{b}} + \sqrt{\sqrt{a} - \sqrt{b}}
$$
is an integer.
a. Must $\sqrt{a}$ be an integer?
b. Must $\sqrt{b}$ be an integer?