# How do you simplify sqrt(-6)+ sqrt(-8)?

Jan 26, 2017

$\sqrt{- 6} + \sqrt{- 8} = i \left(\sqrt{6} + 2 \sqrt{2}\right)$

#### Explanation:

We should remember square root of negative numbers means, we are dealing with complex numbers. Important thing to note here is that $\sqrt{- 1} = i$ or ${i}^{2} = - 1$.

Hence, $\sqrt{- 6} + \sqrt{- 8}$

= $\sqrt{- 1 \times 6} + \sqrt{- 1 \times 8}$

= $\sqrt{- 1} \times \sqrt{6} + \sqrt{- 1} \times \sqrt{2 \times 2 \times 2}$

= $i \sqrt{6} + 2 i \sqrt{2}$

= $i \left(\sqrt{6} + 2 \sqrt{2}\right)$