# How do you simplify (5sqrt3) /( 6sqrt10)?

Jul 25, 2015

You rationalize the denominator and check to see if you can cancel any of the terms out.

#### Explanation:

The first thing you need to do in order to simplify this expression is to rationalize the denominator.

You can do that by multiplying the numerator and the denominator by $\sqrt{10}$

$\frac{5 \cdot \sqrt{3} \cdot \sqrt{10}}{6 \cdot \sqrt{10} \cdot \sqrt{10}}$

Now use the product property of radicals to get

$\frac{5 \cdot \sqrt{3 \cdot 10}}{6 \cdot \sqrt{10 \cdot 10}} = \frac{5 \cdot \sqrt{30}}{6 \cdot 10} = \frac{5 \cdot \sqrt{30}}{6 \cdot 2 \cdot 5}$

This is equivalent to

$\frac{\cancel{5} \cdot \sqrt{30}}{6 \cdot 2 \cdot \cancel{5}} = \textcolor{g r e e n}{\frac{\sqrt{30}}{12}}$