# How do you combine \sqrt { 27} + 3\sqrt { 12} - 9\sqrt { 8}?

Sep 2, 2017

$9 \left(\sqrt{3} - 2 \sqrt{2}\right)$

#### Explanation:

With roots, the best way to approach the simplification is to look for factors that are squares. Let's look at $\sqrt{27}$

$\sqrt{27} = \sqrt{9 \cdot 3}$

9 has a square root, so we can pull its root out from under the radical.

$\sqrt{27} = \sqrt{9 \cdot 3} = 3 \sqrt{3}$

So now let's simplify the other roots the same way:

$3 \sqrt{3} + 3 \sqrt{4 \cdot 3} - 9 \sqrt{4 \cdot 2}$

$3 \sqrt{3} + \left(3 \cdot 2\right) \sqrt{3} - \left(9 \cdot 2\right) \sqrt{2}$

$3 \sqrt{3} + 6 \sqrt{3} - 18 \sqrt{2}$

We can combine the two $\sqrt{3}$ terms.

$9 \sqrt{3} - 18 \sqrt{2}$

Last, if you want, you can pull the common factor of 9 out:

$9 \left(\sqrt{3} - 2 \sqrt{2}\right)$