# How do you simplify (6sqrt20)/(3sqrt5)?

Nov 12, 2015

=color(blue)(4

#### Explanation:

$\frac{6 \sqrt{20}}{3 \sqrt{5}}$

Here, we first simplify $\sqrt{20}$ , by prime factorising $20$

sqrt20=sqrt(5*2*2)=sqrt(5*2^2) = color(blue)(2sqrt5

The expression now becomes:

$\frac{6 \sqrt{20}}{3 \sqrt{5}} = \frac{6 \cdot \textcolor{b l u e}{2 \sqrt{5}}}{3 \sqrt{5}}$

$= \frac{12 \left(\sqrt{5}\right)}{3 \sqrt{5}}$

$= \frac{\cancel{12} \left(\cancel{\sqrt{5}}\right)}{\cancel{3} \cancel{\sqrt{5}}}$

=color(blue)(4

Nov 12, 2015

$4$

#### Explanation:

Let's get the radical out of the denominator by doing the following:

$\frac{6 \sqrt{20}}{3 \sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

$\frac{6 \sqrt{20} \cdot \sqrt{5}}{3 \cdot 5}$

Now we can combine the roots like so:

$\frac{6 \sqrt{100}}{15}$

Now clean it up:

$\frac{2 \sqrt{100}}{5}$

$\frac{2 \cdot 10}{5}$

$\frac{2 \cdot 2}{1}$

$4$