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

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

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{6} is 6.

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

Multiply 4 and 6 to get 24.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{24}{9}$$

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

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$