Solve 1-(frac{5sqrt{7}}{14})^2=

$$1 - ( \frac { 5 \sqrt { 7 } } { 14 } ) ^ { 2 } =$$

Evaluate

$$\frac{3}{28}\approx 0.107142857$$

Solution Steps

To raise \frac{5\sqrt{7}}{14} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(5\sqrt{7}\right)^{2}}{14^{2}}$$

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

$$1-\frac{5^{2}\left(\sqrt{7}\right)^{2}}{14^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$1-\frac{25\left(\sqrt{7}\right)^{2}}{14^{2}}$$

The square of \sqrt{7} is 7.

$$1-\frac{25\times 7}{14^{2}}$$

Multiply 25 and 7 to get 175.

$$1-\frac{175}{14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$1-\frac{175}{196}$$

Reduce the fraction \frac{175}{196} to lowest terms by extracting and canceling out 7.

$$1-\frac{25}{28}$$

Subtract \frac{25}{28} from 1 to get \frac{3}{28}.

$$\frac{3}{28}$$

Factor

$$\frac{3}{2 ^ {2} \cdot 7} = 0.10714285714285714$$