Solve (frac{2sqrt{5}}{5})^2

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

Evaluate

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

Solution Steps

To raise \frac{2\sqrt{5}}{5} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{5} is 5.

$$\frac{4\times 5}{5^{2}}$$

Multiply 4 and 5 to get 20.

$$\frac{20}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{20}{25}$$

Reduce the fraction \frac{20}{25} to lowest terms by extracting and canceling out 5.

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

Factor

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