Solve (frac{2sqrt{13}}{13})^2+(frac{3sqrt{13}}{13})

$$( \frac { 2 \sqrt { 13 } } { 13 } ) ^ { 2 } + ( \frac { 3 \sqrt { 13 } } { 13 } )$$

Evaluate

$$\frac{3\sqrt{13}+4}{13}\approx 1.139742602$$

Short Solution Steps

To raise \frac{2\sqrt{13}}{13} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2\sqrt{13}\right)^{2}}{13^{2}}+\frac{3\sqrt{13}}{13}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 13^{2} and 13 is 169. Multiply \frac{3\sqrt{13}}{13} times \frac{13}{13}.

$$\frac{\left(2\sqrt{13}\right)^{2}}{169}+\frac{13\times 3\sqrt{13}}{169}$$

Since \frac{\left(2\sqrt{13}\right)^{2}}{169} and \frac{13\times 3\sqrt{13}}{169} have the same denominator, add them by adding their numerators.

$$\frac{\left(2\sqrt{13}\right)^{2}+13\times 3\sqrt{13}}{169}$$

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

$$\frac{2^{2}\left(\sqrt{13}\right)^{2}}{13^{2}}+\frac{3\sqrt{13}}{13}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4\left(\sqrt{13}\right)^{2}}{13^{2}}+\frac{3\sqrt{13}}{13}$$

The square of \sqrt{13} is 13.

$$\frac{4\times 13}{13^{2}}+\frac{3\sqrt{13}}{13}$$

Multiply 4 and 13 to get 52.

$$\frac{52}{13^{2}}+\frac{3\sqrt{13}}{13}$$

Calculate 13 to the power of 2 and get 169.

$$\frac{52}{169}+\frac{3\sqrt{13}}{13}$$

Reduce the fraction \frac{52}{169} to lowest terms by extracting and canceling out 13.

$$\frac{4}{13}+\frac{3\sqrt{13}}{13}$$

Since \frac{4}{13} and \frac{3\sqrt{13}}{13} have the same denominator, add them by adding their numerators.

$$\frac{4+3\sqrt{13}}{13}$$

Factor

$$\frac{3 \sqrt{13} + 4}{13} = 1.1397426020301513$$