# How do you simplify 5sqrt(54x )- 3sqrt(96x)?

Apr 13, 2018

$3 \sqrt{6 x}$

Here's how I did it:

#### Explanation:

$5 \sqrt{54 x} - 3 \sqrt{96 x}$

First, we need to radicalize both expressions completely. We need to find a number that can have a root taken of.

For $54$, we know that $9 \cdot 6 = 54$ and that $9 = {3}^{2}$.
For $96$, we know that $16 \cdot 6 = 96$ and that $16 = {4}^{2}$.

Therefore:

$5 \sqrt{9 \cdot 6 x} - 3 \sqrt{16 \cdot 6 x}$

Bring out the number that can be square rooted:
$5 \cdot 3 \cdot \sqrt{6 x} - 3 \cdot 4 \cdot \sqrt{6 x}$

Simplify:
$15 \sqrt{6 x} - 12 \sqrt{6 x}$

Since both radicals have the same value inside the square root, we can subtract the two radicals:
$3 \sqrt{6 x}$

Hope this helps!