Solve 17^2+({left(frac{17sqrt{3}}{3}right)}^2

$${ 17 }^{ 2 } +( { \left( \frac{ 17 \sqrt{ 3 } }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{1156}{3}\approx 385.333333333$$

Solution Steps

Calculate 17 to the power of 2 and get 289.

$$289+\left(\frac{17\sqrt{3}}{3}\right)^{2}$$

To raise \frac{17\sqrt{3}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$289+\frac{\left(17\sqrt{3}\right)^{2}}{3^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 289 times \frac{3^{2}}{3^{2}}.

$$\frac{289\times 3^{2}}{3^{2}}+\frac{\left(17\sqrt{3}\right)^{2}}{3^{2}}$$

Since \frac{289\times 3^{2}}{3^{2}} and \frac{\left(17\sqrt{3}\right)^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

$$\frac{289\times 3^{2}+\left(17\sqrt{3}\right)^{2}}{3^{2}}$$

Expand \left(17\sqrt{3}\right)^{2}.

$$289+\frac{17^{2}\left(\sqrt{3}\right)^{2}}{3^{2}}$$

Calculate 17 to the power of 2 and get 289.

$$289+\frac{289\left(\sqrt{3}\right)^{2}}{3^{2}}$$

The square of \sqrt{3} is 3.

$$289+\frac{289\times 3}{3^{2}}$$

Multiply 289 and 3 to get 867.

$$289+\frac{867}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$289+\frac{867}{9}$$

Reduce the fraction \frac{867}{9} to lowest terms by extracting and canceling out 3.

$$289+\frac{289}{3}$$

Add 289 and \frac{289}{3} to get \frac{1156}{3}.

$$\frac{1156}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 17 ^ {2}}{3} = 385\frac{1}{3} = 385.3333333333333$$