# What is the square root of -340?

##### 1 Answer
Sep 14, 2015

$2 \sqrt{85} i$

#### Explanation:

A negative square root has an imaginary number.

$\sqrt{- 1} = i$

$\sqrt{- 340} =$

$\sqrt{\left(- 1\right) \left(340\right)} =$

$\sqrt{340} i$

Write the prime factors for $340$.

$\sqrt{340} = \left(\sqrt{2 \times 2 \times 5 \times 17}\right)$

Square like terms.

$\sqrt{{2}^{2} \times 5 \times 17} =$

$2 \sqrt{5 \times 17}$

$5$ and $17$ are prime factors, so multiply them and keep them under the square root symbol. Add the symbol for an imaginary number.

$2 \sqrt{85} i$