# How do you simplify sqrt75*sqrt60?

Feb 1, 2016

$30 \sqrt{5}$

#### Explanation:

Recall that a $\textcolor{b l u e}{\text{perfect square}}$ is the product of squaring a whole number.

For example:

${2}^{2} = \textcolor{b l u e}{4}$

${3}^{2} = \textcolor{b l u e}{9}$

${5}^{2} = \textcolor{b l u e}{25}$

${6}^{2} = \textcolor{b l u e}{36}$

When you simplify a radical, you must first break it down using $\textcolor{b l u e}{\text{perfect square}}$ numbers. For example, in your case:

$\sqrt{75} \cdot \sqrt{60}$

$= \sqrt{\textcolor{b l u e}{25} \cdot 3} \cdot \sqrt{\textcolor{b l u e}{4} \cdot 15}$

The square root of $\textcolor{b l u e}{25}$ is $\textcolor{red}{5}$, so you can bring the 25 out of the square root sign and write a $5$ instead. Similarly, the square root of $\textcolor{b l u e}{4}$ is $\textcolor{red}{2}$, so you can also bring the $4$ out of the square root sign and write a $2$ instead.

$= \textcolor{red}{5} \textcolor{g r e e n}{\sqrt{3}} \cdot \textcolor{red}{2} \textcolor{g r e e n}{\sqrt{15}}$

Multiply.

$= \left(\textcolor{red}{5} \cdot \textcolor{red}{2}\right) \left(\textcolor{g r e e n}{\sqrt{3}} \cdot \textcolor{g r e e n}{\sqrt{15}}\right)$

$= 10 \sqrt{45}$

Since $\sqrt{45}$ can be simplified even further:

$= 10 \sqrt{\textcolor{b l u e}{9} \cdot 5}$

Simplify.

$= 10 \cdot \textcolor{red}{3} \sqrt{5}$

$= 30 \sqrt{5}$