# How do you perform the operation and write the result in standard form given (-2+sqrt-8)+(5-sqrt-50)?

Sep 16, 2016

$\left(- 1 + \sqrt{- 8}\right) + \left(5 - \sqrt{- 50}\right) = 4 - 3 \sqrt{2} i$

#### Explanation:

$\left(- 1 + \sqrt{- 8}\right) + \left(5 - \sqrt{- 50}\right)$

= $\left(- 1 + \sqrt{- 2 \times 2 \times 2}\right) + \left(5 - \sqrt{- 2 \times 5 \times 5}\right)$

= $- 1 + 2 \sqrt{2} \times \sqrt{- 1} + 5 - 5 \sqrt{2} \times \sqrt{- 1}$

= $- 1 + 2 \sqrt{2} i + 5 - 5 \sqrt{2} i$

= $4 - 3 \sqrt{2} i$