Solve sqrt{165^2-124^2/164}

$$\sqrt { \frac { 165 ^ { 2 } - 124 ^ { 2 } } { 164 } }$$

Evaluate

$$\frac{17}{2}=8.5$$

Solution Steps

Calculate 165 to the power of 2 and get 27225.

$$\sqrt{\frac{27225-124^{2}}{164}}$$

Calculate 124 to the power of 2 and get 15376.

$$\sqrt{\frac{27225-15376}{164}}$$

Subtract 15376 from 27225 to get 11849.

$$\sqrt{\frac{11849}{164}}$$

Reduce the fraction \frac{11849}{164} to lowest terms by extracting and canceling out 41.

$$\sqrt{\frac{289}{4}}$$

Rewrite the square root of the division \frac{289}{4} as the division of square roots \frac{\sqrt{289}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{17}{2}$$

Factor

$$\frac{17}{2} = 8\frac{1}{2} = 8.5$$