Solve sqrt{(20/3)^2+5^2}

$$\sqrt { ( \frac { 20 } { 3 } ) ^ { 2 } + 5 ^ { 2 } }$$

Evaluate

$$\frac{25}{3}\approx 8.333333333$$

Solution Steps

Calculate \frac{20}{3} to the power of 2 and get \frac{400}{9}.

$$\sqrt{\frac{400}{9}+5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{400}{9}+25}$$

Convert 25 to fraction \frac{225}{9}.

$$\sqrt{\frac{400}{9}+\frac{225}{9}}$$

Since \frac{400}{9} and \frac{225}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{400+225}{9}}$$

Add 400 and 225 to get 625.

$$\sqrt{\frac{625}{9}}$$

Rewrite the square root of the division \frac{625}{9} as the division of square roots \frac{\sqrt{625}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{25}{3}$$

Factor

$$\frac{5 ^ {2}}{3} = 8\frac{1}{3} = 8.333333333333334$$