Solve (frac{8sqrt{3}}{15})^2+(8/5)^2

$$( \frac { 8 \sqrt { 3 } } { 15 } ) ^ { 2 } + ( \frac { 8 } { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{256}{75}\approx 3.413333333$$

Solution Steps

To raise \frac{8\sqrt{3}}{15} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(8\sqrt{3}\right)^{2}}{15^{2}}+\left(\frac{8}{5}\right)^{2}$$

Calculate \frac{8}{5} to the power of 2 and get \frac{64}{25}.

$$\frac{\left(8\sqrt{3}\right)^{2}}{15^{2}}+\frac{64}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15^{2} and 25 is 225. Multiply \frac{64}{25} times \frac{9}{9}.

$$\frac{\left(8\sqrt{3}\right)^{2}}{225}+\frac{64\times 9}{225}$$

Since \frac{\left(8\sqrt{3}\right)^{2}}{225} and \frac{64\times 9}{225} have the same denominator, add them by adding their numerators.

$$\frac{\left(8\sqrt{3}\right)^{2}+64\times 9}{225}$$

Expand \left(8\sqrt{3}\right)^{2}.

$$\frac{8^{2}\left(\sqrt{3}\right)^{2}}{15^{2}}+\frac{64}{25}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64\left(\sqrt{3}\right)^{2}}{15^{2}}+\frac{64}{25}$$

The square of \sqrt{3} is 3.

$$\frac{64\times 3}{15^{2}}+\frac{64}{25}$$

Multiply 64 and 3 to get 192.

$$\frac{192}{15^{2}}+\frac{64}{25}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{192}{225}+\frac{64}{25}$$

Reduce the fraction \frac{192}{225} to lowest terms by extracting and canceling out 3.

$$\frac{64}{75}+\frac{64}{25}$$

Add \frac{64}{75} and \frac{64}{25} to get \frac{256}{75}.

$$\frac{256}{75}$$

Factor

$$\frac{2 ^ {8}}{3 \cdot 5 ^ {2}} = 3\frac{31}{75} = 3.4133333333333336$$