Solve 1-(frac{7sqrt{5}}{20})^2

$$1 - ( \frac { 7 \sqrt { 5 } } { 20 } ) ^ { 2 }$$

Evaluate

$$\frac{31}{80}=0.3875$$

Solution Steps

To raise \frac{7\sqrt{5}}{20} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(7\sqrt{5}\right)^{2}}{20^{2}}$$

Expand \left(7\sqrt{5}\right)^{2}.

$$1-\frac{7^{2}\left(\sqrt{5}\right)^{2}}{20^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$1-\frac{49\left(\sqrt{5}\right)^{2}}{20^{2}}$$

The square of \sqrt{5} is 5.

$$1-\frac{49\times 5}{20^{2}}$$

Multiply 49 and 5 to get 245.

$$1-\frac{245}{20^{2}}$$

Calculate 20 to the power of 2 and get 400.

$$1-\frac{245}{400}$$

Reduce the fraction \frac{245}{400} to lowest terms by extracting and canceling out 5.

$$1-\frac{49}{80}$$

Subtract \frac{49}{80} from 1 to get \frac{31}{80}.

$$\frac{31}{80}$$

Factor

$$\frac{31}{2 ^ {4} \cdot 5} = 0.3875$$