Solve (frac{14sqrt{6}}{65})^2

$$( \frac { 14 \sqrt { 6 } } { 65 } ) ^ { 2 }$$

Evaluate

$$\frac{1176}{4225}\approx 0.278343195$$

Solution Steps

To raise \frac{14\sqrt{6}}{65} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(14\sqrt{6}\right)^{2}}{65^{2}}$$

Expand \left(14\sqrt{6}\right)^{2}.

$$\frac{14^{2}\left(\sqrt{6}\right)^{2}}{65^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$\frac{196\left(\sqrt{6}\right)^{2}}{65^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{196\times 6}{65^{2}}$$

Multiply 196 and 6 to get 1176.

$$\frac{1176}{65^{2}}$$

Calculate 65 to the power of 2 and get 4225.

$$\frac{1176}{4225}$$

Factor

$$\frac{2 ^ {3} \cdot 3 \cdot 7 ^ {2}}{5 ^ {2} \cdot 13 ^ {2}} = 0.2783431952662722$$