# How do you evaluate \sqrt ( ( - 1- 2) ^ ( 2) + ( 2- ( - 4) ^ ( 2) ) )?

Sep 14, 2017

$\sqrt{5} i$

#### Explanation:

We have: $\sqrt{{\left(- 1 - 2\right)}^{2} + \left(2 - {\left(- 4\right)}^{2}\right)}$

Let's evaluate the expressions within the parentheses:

$= \sqrt{{\left(- 3\right)}^{2} + \left(2 - 16\right)}$

$= \sqrt{9 + \left(- 14\right)}$

$= \sqrt{- 5}$

Then, let's express the number underneath the square root function as a product:

$= \sqrt{- 1 \times 5}$

Using the rules of surds:

$= \sqrt{- 1} \times \sqrt{5}$

$\sqrt{- 1}$ is the imaginary unit $i$ in mathematics.

$= i \times \sqrt{5}$

$= \sqrt{5} i$