Solve 5/2sqrt{1/5}+3sqrt{5}

$$\frac{ 5 }{ 2 } \sqrt{ \frac{ 1 }{ 5 } } +3 \sqrt{ 5 }$$

Evaluate

$$\frac{7\sqrt{5}}{2}\approx 7.826237921$$

Solution Steps

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

$$\frac{5}{2}\times \frac{\sqrt{1}}{\sqrt{5}}+3\sqrt{5}$$

Calculate the square root of 1 and get 1.

$$\frac{5}{2}\times \frac{1}{\sqrt{5}}+3\sqrt{5}$$

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

$$\frac{5}{2}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+3\sqrt{5}$$

The square of \sqrt{5} is 5.

$$\frac{5}{2}\times \frac{\sqrt{5}}{5}+3\sqrt{5}$$

Multiply \frac{5}{2} times \frac{\sqrt{5}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\sqrt{5}}{2\times 5}+3\sqrt{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\sqrt{5}}{2}+3\sqrt{5}$$

Combine \frac{\sqrt{5}}{2} and 3\sqrt{5} to get \frac{7}{2}\sqrt{5}.

$$\frac{7}{2}\sqrt{5}$$