Solve sqrt{82^2/100+93^2/100}

$$\sqrt { \frac { 82 ^ { 2 } } { 100 } + \frac { 93 ^ { 2 } } { 100 } }$$

Evaluate

$$\frac{\sqrt{15373}}{10}\approx 12.398790264$$

Solution Steps

Calculate 82 to the power of 2 and get 6724.

$$\sqrt{\frac{6724}{100}+\frac{93^{2}}{100}}$$

Reduce the fraction \frac{6724}{100} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{1681}{25}+\frac{93^{2}}{100}}$$

Calculate 93 to the power of 2 and get 8649.

$$\sqrt{\frac{1681}{25}+\frac{8649}{100}}$$

Least common multiple of 25 and 100 is 100. Convert \frac{1681}{25} and \frac{8649}{100} to fractions with denominator 100.

$$\sqrt{\frac{6724}{100}+\frac{8649}{100}}$$

Since \frac{6724}{100} and \frac{8649}{100} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{6724+8649}{100}}$$

Add 6724 and 8649 to get 15373.

$$\sqrt{\frac{15373}{100}}$$

Rewrite the square root of the division \sqrt{\frac{15373}{100}} as the division of square roots \frac{\sqrt{15373}}{\sqrt{100}}.

$$\frac{\sqrt{15373}}{\sqrt{100}}$$

Calculate the square root of 100 and get 10.

$$\frac{\sqrt{15373}}{10}$$