Solve {left(frac{34sqrt{3}}{3}right)}^2

$${ \left( \frac{ 34 \sqrt{ 3 } }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{1156}{3}\approx 385.333333333$$

Solution Steps

To raise \frac{34\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(34\sqrt{3}\right)^{2}}{3^{2}}$$

Expand \left(34\sqrt{3}\right)^{2}.

$$\frac{34^{2}\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Calculate 34 to the power of 2 and get 1156.

$$\frac{1156\left(\sqrt{3}\right)^{2}}{3^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{1156\times 3}{3^{2}}$$

Multiply 1156 and 3 to get 3468.

$$\frac{3468}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{3468}{9}$$

Reduce the fraction \frac{3468}{9} to lowest terms by extracting and canceling out 3.

$$\frac{1156}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 17 ^ {2}}{3} = 385\frac{1}{3} = 385.3333333333333$$