# How do you simplify sqrt((-3)(-12))?

Feb 19, 2017

$\sqrt{\left(- 3\right) \left(- 12\right)} = 6$

#### Explanation:

$\sqrt{\left(- 3\right) \left(- 12\right)} = \sqrt{36} = \sqrt{{6}^{2}} = 6$

What is interesting here is what you must not do:

$\sqrt{\left(- 3\right) \left(- 12\right)} \ne \sqrt{- 3} \sqrt{- 12} = i \sqrt{3} \cdot i \sqrt{12} = {i}^{2} \sqrt{36} = - 6$

Note that for Real values of $a , b$, the identity:

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

only holds when at least one of $a , b$ is non-negative.