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

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

Evaluate

$$\frac{3}{5}=0.6$$

Solution Steps

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

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

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

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

The square of \sqrt{5} is 5.

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

Calculate 5 to the power of 2 and get 25.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5^{2} and 5 is 25. Multiply \frac{1}{5} times \frac{5}{5}.

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

Since \frac{\left(2\sqrt{5}\right)^{2}}{25} and \frac{5}{25} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$\frac{4\left(\sqrt{5}\right)^{2}}{5^{2}}-\frac{1}{5}$$

The square of \sqrt{5} is 5.

$$\frac{4\times 5}{5^{2}}-\frac{1}{5}$$

Multiply 4 and 5 to get 20.

$$\frac{20}{5^{2}}-\frac{1}{5}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{20}{25}-\frac{1}{5}$$

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

$$\frac{4}{5}-\frac{1}{5}$$

Subtract \frac{1}{5} from \frac{4}{5} to get \frac{3}{5}.

$$\frac{3}{5}$$

Factor

$$\frac{3}{5} = 0.6$$