# What is the square root of 12 multiplied by the square root of 6?

Sep 17, 2015

$\sqrt{12} \sqrt{6} = 6 \sqrt{2}$

#### Explanation:

To evaluate $\sqrt{12} \sqrt{6}$ we must first remember that we can join these two roots together

$\sqrt{a} \sqrt{b} = \sqrt{a b}$ as long as they're not both negative, so
$\sqrt{12} \sqrt{6} = \sqrt{12 \cdot 6}$

While we can just multiply these two, we know that $12 = 2 \cdot 6$, so we know that $12 \cdot 6 = 2 \cdot 6 \cdot 6 = 2 \cdot {6}^{2}$

Therefore $\sqrt{12 \cdot 6} = \sqrt{2 \cdot {6}^{2}}$.
Now, since there's no additions or differences being done we can take it out of the root, but to get out it loses its square. So

$\sqrt{12} \sqrt{6} = 6 \sqrt{2}$

And now there's no more manipulation to be done.