Solve 4-(frac{2sqrt{6}}{3})^2

$$4 - ( \frac { 2 \sqrt { 6 } } { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{4}{3}\approx 1.333333333$$

Solution Steps

To raise \frac{2\sqrt{6}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$4-\frac{\left(2\sqrt{6}\right)^{2}}{3^{2}}$$

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

$$4-\frac{2^{2}\left(\sqrt{6}\right)^{2}}{3^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$4-\frac{4\left(\sqrt{6}\right)^{2}}{3^{2}}$$

The square of \sqrt{6} is 6.

$$4-\frac{4\times 6}{3^{2}}$$

Multiply 4 and 6 to get 24.

$$4-\frac{24}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$4-\frac{24}{9}$$

Reduce the fraction \frac{24}{9} to lowest terms by extracting and canceling out 3.

$$4-\frac{8}{3}$$

Subtract \frac{8}{3} from 4 to get \frac{4}{3}.

$$\frac{4}{3}$$

Factor

$$\frac{2 ^ {2}}{3} = 1\frac{1}{3} = 1.3333333333333333$$