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

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

Evaluate

$$\frac{4}{5}=0.8$$

Solution Steps

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

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

The square of \sqrt{5} is 5.

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

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

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

Expand \left(\frac{2}{5}\sqrt{5}\right)^{2}.

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

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{4}{25}\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$\frac{4}{25}\times 5$$

Multiply \frac{4}{25} and 5 to get \frac{4}{5}.

$$\frac{4}{5}$$

Factor

$$\frac{2 ^ {2}}{5} = 0.8$$