Question

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

Answer 1

Cancel out what is common in the numerator and denominator, then simplify the result and get to
`2sqrt(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:

`120/5 = (24*5)/5 = 24`

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

`sqrt(120)/sqrt(5) = sqrt(24*5)/sqrt(5) = (sqrt(24)*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*6) = sqrt(4)*sqrt(6) = 2sqrt(6)`