# How do you simplify the radical expression: sqrt 120 / sqrt 5?

Cancel out what is common in the numerator and denominator, then simplify the result and get to
$2 \sqrt{6}$

#### Explanation:

Questions like this one require that we find something in the numerator and something in the denominator that are the same, then we cancel them out and get a simplified expression.

Before we dive in, let's look at the fraction. Let's ignore the square roots for the moment! In the denominator there is a 5. In the numerator there is a 120. Can we evenly divide 5 into 120? Yes - 5 goes into 120 24 times. So if there wasn't the square roots, things would look like this:

$\frac{120}{5} = \frac{24 \cdot 5}{5} = 24$

With both the numerator and denominator having square roots, the above will work the same way:

$\frac{\sqrt{120}}{\sqrt{5}} = \frac{\sqrt{24 \cdot 5}}{\sqrt{5}} = \frac{\sqrt{24} \cdot \sqrt{5}}{\sqrt{5}} = \sqrt{24}$

Now we can simplify $\sqrt{24}$. We do that by finding a perfect square as a factor of the number in the square root (if there isn't one, we're done). Is there one? Yes! 4 is a perfect square.

$\sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2 \sqrt{6}$