Solve 6^2-(frac{6sqrt{5}}{5})^2

$$6 ^ { 2 } - ( \frac { 6 \sqrt { 5 } } { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{144}{5}=28.8$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$36-\left(\frac{6\sqrt{5}}{5}\right)^{2}$$

To raise \frac{6\sqrt{5}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$36-\frac{\left(6\sqrt{5}\right)^{2}}{5^{2}}$$

Expand \left(6\sqrt{5}\right)^{2}.

$$36-\frac{6^{2}\left(\sqrt{5}\right)^{2}}{5^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$36-\frac{36\left(\sqrt{5}\right)^{2}}{5^{2}}$$

The square of \sqrt{5} is 5.

$$36-\frac{36\times 5}{5^{2}}$$

Multiply 36 and 5 to get 180.

$$36-\frac{180}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$36-\frac{180}{25}$$

Reduce the fraction \frac{180}{25} to lowest terms by extracting and canceling out 5.

$$36-\frac{36}{5}$$

Subtract \frac{36}{5} from 36 to get \frac{144}{5}.

$$\frac{144}{5}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2}}{5} = 28\frac{4}{5} = 28.8$$