Solve sqrt{8^2+(32/3)^2}

$$\sqrt { 8 ^ { 2 } + ( \frac { 32 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{40}{3}\approx 13.333333333$$

Solution Steps

Calculate 8 to the power of 2 and get 64.

$$\sqrt{64+\left(\frac{32}{3}\right)^{2}}$$

Calculate \frac{32}{3} to the power of 2 and get \frac{1024}{9}.

$$\sqrt{64+\frac{1024}{9}}$$

Convert 64 to fraction \frac{576}{9}.

$$\sqrt{\frac{576}{9}+\frac{1024}{9}}$$

Since \frac{576}{9} and \frac{1024}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{576+1024}{9}}$$

Add 576 and 1024 to get 1600.

$$\sqrt{\frac{1600}{9}}$$

Rewrite the square root of the division \frac{1600}{9} as the division of square roots \frac{\sqrt{1600}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{40}{3}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{3} = 13\frac{1}{3} = 13.333333333333334$$