# How do you simplify sqrt33-sqrt9?

##### 1 Answer

Find what is common in the 2 expressions, then factor it out to get to
$\sqrt{3} \cdot \left(\sqrt{11} - \sqrt{3}\right)$

#### Explanation:

When we look to "simplify", most times we are looking to combine the terms in a different way than the one presented.

Take this question for example - we want to find a way to combine the two square roots into one expression. To do that, we need to find what is common about them.

$\sqrt{33} - \sqrt{9}$

let's break down the 33 and 9 into they're respective factors

$\sqrt{11 \cdot 3} - \sqrt{3 \cdot 3}$

and I can express this in a different way

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

Each expression has a $\sqrt{3}$, so let's factor that out

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

And that is the final answer (remember that $\sqrt{11}$ and $\sqrt{3}$ are different numbers, so can't simply be subtracted to get $\sqrt{8}$)