Question

How do I solve this?

Answer 1

Start with

$4i\sqrt{5}$

Since square root and square are two opposite operations, we have

$4i = \sqrt{(4i)^2} = \sqrt{-16}$

So, we have

$4i\sqrt{5} = \sqrt{-16}\cdot\sqrt{5}$

Use the rule $\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$ to conclude

$\sqrt{-16}\cdot\sqrt{5} = \sqrt{-16\cdot 5} = \sqrt{-80}$