Solve (frac{25sqrt{13}}{26})^2+9

$$( \frac { 25 \sqrt { 13 } } { 26 } ) ^ { 2 } + 9$$

Evaluate

$$\frac{1093}{52}\approx 21.019230769$$

Solution Steps

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

$$\frac{\left(25\sqrt{13}\right)^{2}}{26^{2}}+9$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{26^{2}}{26^{2}}.

$$\frac{\left(25\sqrt{13}\right)^{2}}{26^{2}}+\frac{9\times 26^{2}}{26^{2}}$$

Since \frac{\left(25\sqrt{13}\right)^{2}}{26^{2}} and \frac{9\times 26^{2}}{26^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(25\sqrt{13}\right)^{2}+9\times 26^{2}}{26^{2}}$$

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

$$\frac{25^{2}\left(\sqrt{13}\right)^{2}}{26^{2}}+9$$

Calculate 25 to the power of 2 and get 625.

$$\frac{625\left(\sqrt{13}\right)^{2}}{26^{2}}+9$$

The square of \sqrt{13} is 13.

$$\frac{625\times 13}{26^{2}}+9$$

Multiply 625 and 13 to get 8125.

$$\frac{8125}{26^{2}}+9$$

Calculate 26 to the power of 2 and get 676.

$$\frac{8125}{676}+9$$

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

$$\frac{625}{52}+9$$

Add \frac{625}{52} and 9 to get \frac{1093}{52}.

$$\frac{1093}{52}$$

Factor

$$\frac{1093}{2 ^ {2} \cdot 13} = 21\frac{1}{52} = 21.01923076923077$$