Solve 1-(frac{3sqrt{3}}{14})^2

$$1 - ( \frac { 3 \sqrt { 3 } } { 14 } ) ^ { 2 }$$

Evaluate

$$\frac{169}{196}\approx 0.862244898$$

Solution Steps

To raise \frac{3\sqrt{3}}{14} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(3\sqrt{3}\right)^{2}}{14^{2}}$$

Expand \left(3\sqrt{3}\right)^{2}.

$$1-\frac{3^{2}\left(\sqrt{3}\right)^{2}}{14^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$1-\frac{9\left(\sqrt{3}\right)^{2}}{14^{2}}$$

The square of \sqrt{3} is 3.

$$1-\frac{9\times 3}{14^{2}}$$

Multiply 9 and 3 to get 27.

$$1-\frac{27}{14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$1-\frac{27}{196}$$

Subtract \frac{27}{196} from 1 to get \frac{169}{196}.

$$\frac{169}{196}$$

Factor

$$\frac{13 ^ {2}}{2 ^ {2} \cdot 7 ^ {2}} = 0.8622448979591837$$