Solve 1-(frac{8sqrt{3}}{13})^2=

$$1 - ( \frac { 8 \sqrt { 3 } } { 13 } ) ^ { 2 } =$$

Evaluate

$$-\frac{23}{169}\approx -0.136094675$$

Solution Steps

To raise \frac{8\sqrt{3}}{13} to a power, raise both numerator and denominator to the power and then divide.

$$1-\frac{\left(8\sqrt{3}\right)^{2}}{13^{2}}$$

Expand \left(8\sqrt{3}\right)^{2}.

$$1-\frac{8^{2}\left(\sqrt{3}\right)^{2}}{13^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$1-\frac{64\left(\sqrt{3}\right)^{2}}{13^{2}}$$

The square of \sqrt{3} is 3.

$$1-\frac{64\times 3}{13^{2}}$$

Multiply 64 and 3 to get 192.

$$1-\frac{192}{13^{2}}$$

Calculate 13 to the power of 2 and get 169.

$$1-\frac{192}{169}$$

Subtract \frac{192}{169} from 1 to get -\frac{23}{169}.

$$-\frac{23}{169}$$

Factor

$$-\frac{23}{169} = -0.13609467455621302$$