Solve (sqrt{1/5}+2sqrt{5})sqrt{5}=

$$( \sqrt { \frac { 1 } { 5 } } + 2 \sqrt { 5 } ) \sqrt { 5 } =$$

Evaluate

$$11$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$\left(\frac{\sqrt{1}}{\sqrt{5}}+2\sqrt{5}\right)\sqrt{5}$$

Calculate the square root of 1 and get 1.

$$\left(\frac{1}{\sqrt{5}}+2\sqrt{5}\right)\sqrt{5}$$

Rationalize the denominator of \frac{1}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\left(\frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+2\sqrt{5}\right)\sqrt{5}$$

The square of \sqrt{5} is 5.

$$\left(\frac{\sqrt{5}}{5}+2\sqrt{5}\right)\sqrt{5}$$

Combine \frac{\sqrt{5}}{5} and 2\sqrt{5} to get \frac{11}{5}\sqrt{5}.

$$\frac{11}{5}\sqrt{5}\sqrt{5}$$

Multiply \sqrt{5} and \sqrt{5} to get 5.

$$\frac{11}{5}\times 5$$

Cancel out 5 and 5.

$$11$$

Factor

$$11$$