Question

Find the domain of the function $$f(x)=\sqrt{3+5-\sqrt{x}}.$$

Answer 1

The stuff under the first or outermost square root needs to be nonnegative.

`3+5-√(x) \ge 0\\\\8-√(x) \ge 0\\\\8 \ge √(x)\\\\√(x) \le 8\\\\x \le 8^2\\\\x \le 64\\\\`

Also, we need to have
`x \ge 0` aka
`0 \le x` so the stuff under the second square root is also nonnegative.

Glue together
`0 \le x \ \text{ and } \ x \le 64` to end up with
`0 \le x \le 64` as the domain.