Solve sqrt{(16)^2+(12)^2+(32/3)^2}

$$\sqrt { ( 16 ) ^ { 2 } + ( 12 ) ^ { 2 } + ( \frac { 32 } { 3 } ) ^ { 2 } }$$

Evaluate

$$\frac{68}{3}\approx 22.666666667$$

Solution Steps

Calculate 16 to the power of 2 and get 256.

$$\sqrt{256+12^{2}+\left(\frac{32}{3}\right)^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\sqrt{256+144+\left(\frac{32}{3}\right)^{2}}$$

Add 256 and 144 to get 400.

$$\sqrt{400+\left(\frac{32}{3}\right)^{2}}$$

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

$$\sqrt{400+\frac{1024}{9}}$$

Convert 400 to fraction \frac{3600}{9}.

$$\sqrt{\frac{3600}{9}+\frac{1024}{9}}$$

Since \frac{3600}{9} and \frac{1024}{9} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{3600+1024}{9}}$$

Add 3600 and 1024 to get 4624.

$$\sqrt{\frac{4624}{9}}$$

Rewrite the square root of the division \frac{4624}{9} as the division of square roots \frac{\sqrt{4624}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{68}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 17}{3} = 22\frac{2}{3} = 22.666666666666668$$