# How do you simplify 2sqrt33 - sqrt30?

Apr 9, 2018

$2 \sqrt{3} \left(\sqrt{11} - \sqrt{10}\right)$

#### Explanation:

The key is to factor the numbers under the square roots and try to find a factor that is a perfect square.

For $33$, the factors are $1 , 3 , 11 , 33$. Since none of these are perfect squares, we cannot simplify it.

For $30$, the factors are $1 , 3 , 5 , 6 , 10 , 30$. Since none of these are perfect squares, we cannot simplify it.

Hence, $2 \sqrt{33} - \sqrt{30}$ is already pretty simplified.

There is one thing that you might do to "simplify", but I don't see the benefit.

You could identify that $3$ is a common factor of both $30$ and $33$. This allows you to factor out a $\sqrt{3}$. You would get:

$2 \sqrt{3} \left(\sqrt{11} - \sqrt{10}\right)$