# How do you perform the operation and write the result in standard form given sqrt(-6)*sqrt(-2)?

Oct 4, 2016

$\sqrt{- 6} \cdot \sqrt{- 2} = - 2 \sqrt{3}$

#### Explanation:

Be a little careful!

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

$\textcolor{w h i t e}{\sqrt{- 6} \cdot \sqrt{- 2}} = \sqrt{6} \sqrt{2} \cdot {i}^{2}$

$\textcolor{w h i t e}{\sqrt{- 6} \cdot \sqrt{- 2}} = - \sqrt{6 \cdot 2}$

$\textcolor{w h i t e}{\sqrt{- 6} \cdot \sqrt{- 2}} = - \sqrt{{2}^{2} \cdot 3}$

$\textcolor{w h i t e}{\sqrt{- 6} \cdot \sqrt{- 2}} = - 2 \sqrt{3}$

Note that if $a < 0$ and $b < 0$ then:

$\sqrt{a} \sqrt{b} = - \sqrt{a b} \ne \sqrt{a b}$