Solve sqrt{(78/60)-(-2/60)^2}*10

$$\sqrt { ( \frac { 78 } { 60 } ) - ( \frac { - 2 } { 60 } ) ^ { 2 } } \times 10$$

Evaluate

$$\frac{\sqrt{1169}}{3}\approx 11.396880665$$

Solution Steps

Reduce the fraction \frac{78}{60} to lowest terms by extracting and canceling out 6.

$$10\sqrt{\frac{13}{10}-\left(\frac{-2}{60}\right)^{2}}$$

Reduce the fraction \frac{-2}{60} to lowest terms by extracting and canceling out 2.

$$10\sqrt{\frac{13}{10}-\left(-\frac{1}{30}\right)^{2}}$$

Calculate -\frac{1}{30} to the power of 2 and get \frac{1}{900}.

$$10\sqrt{\frac{13}{10}-\frac{1}{900}}$$

Subtract \frac{1}{900} from \frac{13}{10} to get \frac{1169}{900}.

$$10\sqrt{\frac{1169}{900}}$$

Rewrite the square root of the division \sqrt{\frac{1169}{900}} as the division of square roots \frac{\sqrt{1169}}{\sqrt{900}}.

$$10\times \frac{\sqrt{1169}}{\sqrt{900}}$$

Calculate the square root of 900 and get 30.

$$10\times \frac{\sqrt{1169}}{30}$$

Cancel out 30, the greatest common factor in 10 and 30.

$$\frac{\sqrt{1169}}{3}$$