Question

Which of the following square root of -80

Answer 1

You can factor -80 as

$-80 = (-1)\cdot 16 \cdot 5$

So, we have

$\sqrt{-80} = \sqrt{(-1)\cdot 16 \cdot 5}$

The square root of a product is the product of the square roots:

$\sqrt{-80} = \sqrt{(-1)}\sqrt{16}\sqrt{5}$

Since $i^2=-1$ and $4^2=16$, we have

$\sqrt{-80} = 4i\sqrt{5}$