Simplify square root fraction

[TigerLittle]

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.
Please help.

[Baltuilhe]

Good afternoon!

[tex]\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}}[/tex]

[tex]=\dfrac{10\sqrt{5}}{\left(\sqrt{5}\right)^2}+\sqrt{4}\times\sqrt{5}=\dfrac{10\sqrt{5}}{5}+2\sqrt{5}[/tex]

[tex]=\dfrac{\cancel{10}^2\sqrt{5}}{\cancel{5}}+2\sqrt{5}=2\sqrt{5}+2\sqrt{5}=\color{blue}\boxed{4\sqrt{5}}[/tex]

I hope to have helped u!

[Guest]

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