Solve frac{sqrt{85^2-84^2}}{sqrt{36}}-1/6

$$\frac { \sqrt { 85 ^ { 2 } - 84 ^ { 2 } } } { \sqrt { 36 } } - \frac { 1 } { 6 }$$

Evaluate

$$2$$

Solution Steps

Calculate 85 to the power of 2 and get 7225.

$$\frac{\sqrt{7225-84^{2}}}{\sqrt{36}}-\frac{1}{6}$$

Calculate 84 to the power of 2 and get 7056.

$$\frac{\sqrt{7225-7056}}{\sqrt{36}}-\frac{1}{6}$$

Subtract 7056 from 7225 to get 169.

$$\frac{\sqrt{169}}{\sqrt{36}}-\frac{1}{6}$$

Calculate the square root of 169 and get 13.

$$\frac{13}{\sqrt{36}}-\frac{1}{6}$$

Calculate the square root of 36 and get 6.

$$\frac{13}{6}-\frac{1}{6}$$

Since \frac{13}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13-1}{6}$$

Subtract 1 from 13 to get 12.

$$\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$2$$

Factor

$$2$$