# How do you simplify sqrt70 ÷ sqrt10?

Aug 11, 2015

$\sqrt{7}$

#### Explanation:

You can actually simplify this expression by using the product property and the quotient property of radicals.

• using the product property

The product property tells you that you have

$\textcolor{b l u e}{\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}}$

In your case, you can write sqrt(70 as

$\sqrt{70} = \sqrt{7 \cdot 10} = \sqrt{7} \cdot \sqrt{10}$

This means that the expression can be simplified to

$\frac{\sqrt{70}}{\sqrt{10}} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{10}}}} \cdot \sqrt{7}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{\sqrt{10}}}}} = \textcolor{g r e e n}{\sqrt{7}}$

• using the quotient property

The quotient property tells you that you have

$\textcolor{b l u e}{\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}}$, where $\sqrt{b} \ne 0$

In your case, you can write

$\frac{\sqrt{70}}{\sqrt{10}} = \sqrt{\frac{70}{10}} = \sqrt{\frac{7 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}}}} = \textcolor{g r e e n}{\sqrt{7}}$