Solve sqrt{1100/1000}*60

$$\sqrt{ \frac{ 1100 }{ 1000 } } \times 60$$

Evaluate

$$6\sqrt{110}\approx 62.92853089$$

Solution Steps

Reduce the fraction \frac{1100}{1000} to lowest terms by extracting and canceling out 100.

$$60\sqrt{\frac{11}{10}}$$

Rewrite the square root of the division \sqrt{\frac{11}{10}} as the division of square roots \frac{\sqrt{11}}{\sqrt{10}}.

$$60\times \frac{\sqrt{11}}{\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$60\times \frac{\sqrt{11}\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$60\times \frac{\sqrt{11}\sqrt{10}}{10}$$

To multiply \sqrt{11} and \sqrt{10}, multiply the numbers under the square root.

$$60\times \frac{\sqrt{110}}{10}$$

Cancel out 10, the greatest common factor in 60 and 10.

$$6\sqrt{110}$$