Solve (frac{25sqrt{13}}{26})^2

$$( \frac { 25 \sqrt { 13 } } { 26 } ) ^ { 2 }$$

Evaluate

$$\frac{625}{52}\approx 12.019230769$$

Solution Steps

To raise \frac{25\sqrt{13}}{26} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(25\sqrt{13}\right)^{2}}{26^{2}}$$

Expand \left(25\sqrt{13}\right)^{2}.

$$\frac{25^{2}\left(\sqrt{13}\right)^{2}}{26^{2}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{625\left(\sqrt{13}\right)^{2}}{26^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{625\times 13}{26^{2}}$$

Multiply 625 and 13 to get 8125.

$$\frac{8125}{26^{2}}$$

Calculate 26 to the power of 2 and get 676.

$$\frac{8125}{676}$$

Reduce the fraction \frac{8125}{676} to lowest terms by extracting and canceling out 13.

$$\frac{625}{52}$$

Factor

$$\frac{5 ^ {4}}{2 ^ {2} \cdot 13} = 12\frac{1}{52} = 12.01923076923077$$