# Simplify square root fraction

### Simplify square root fraction

Hi
I have to simplify this square root fraction:
10/√5+√20

The answer is 4√5, but I do not get to that answer.
TigerLittle

Posts: 1
Joined: Thu Jul 25, 2019 3:15 pm
Reputation: 0

### Re: Simplify square root fraction

Good afternoon!

$$\dfrac{10}{\sqrt{5}}+\sqrt{20}=\dfrac{10}{\sqrt{5}}\overbrace{\left(\times\dfrac{\sqrt{5}}{\sqrt{5}}\right)}^{\times 1}+\sqrt{\underbrace{4\times 5}_{20}}$$

$$=\dfrac{10\sqrt{5}}{\left(\sqrt{5}\right)^2}+\sqrt{4}\times\sqrt{5}=\dfrac{10\sqrt{5}}{5}+2\sqrt{5}$$

$$=\dfrac{\cancel{10}^2\sqrt{5}}{\cancel{5}}+2\sqrt{5}=2\sqrt{5}+2\sqrt{5}=\color{blue}\boxed{4\sqrt{5}}$$

I hope to have helped u!

Baltuilhe

Posts: 35
Joined: Fri Dec 14, 2018 3:55 pm
Reputation: 26

### Re: Simplify square root fraction

What you have written, "$$10/\sqrt{5}+ \sqrt{20}$$" is correctly $$\frac{10}{\sqrt{5}+ \sqrt{20}}$$ but some might have written that when they meant $$10/(\sqrt{5}+ \sqrt{20})= \frac{10}{\sqrt{5}+ \sqrt{20}}$$. In that case, since $$\sqrt{20}= \sqrt{4(5)}= 2\sqrt{5}$$, we can write $$\frac{10}{3\sqrt{5}}$$ and, rationalizing the denominator $$\frac{10\sqrt{5}}{5}$$.
Guest