Solve =sqrt{(85/3)^2-17^2}

$$= \sqrt { ( \frac { 85 } { 3 } ) ^ { 2 } - 17 ^ { 2 } }$$

Evaluate

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

Solution Steps

Calculate \frac{85}{3} to the power of 2 and get \frac{7225}{9}.

$$\sqrt{\frac{7225}{9}-17^{2}}$$

Calculate 17 to the power of 2 and get 289.

$$\sqrt{\frac{7225}{9}-289}$$

Convert 289 to fraction \frac{2601}{9}.

$$\sqrt{\frac{7225}{9}-\frac{2601}{9}}$$

Since \frac{7225}{9} and \frac{2601}{9} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{7225-2601}{9}}$$

Subtract 2601 from 7225 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

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