# How do you find the square root of -59?

$\sqrt{- 59} = \sqrt{\left(- 1\right) \left(59\right)} = \sqrt{- 1} \sqrt{59} = i \sqrt{59}$

#### Explanation:

$\sqrt{- 59} = \sqrt{\left(- 1\right) \left(59\right)} = \sqrt{- 1} \sqrt{59}$

We can now look at each square root separately.

$\sqrt{- 1}$

We use the nomenclature $i$, and so $\sqrt{- 1} = i$

$\sqrt{59}$

The number 59 is prime, meaning it has no factors other than itself and one. Therefore it can't be broken down to anything smaller.

So we end up with:

$\sqrt{- 59} = \sqrt{\left(- 1\right) \left(59\right)} = \sqrt{- 1} \sqrt{59} = i \sqrt{59}$