Solve sqrt{(2)(106.51)/(20)}rightarrowsqrt{213.02/20}rightarrowsqrt{10.65}

$$\sqrt { \frac { ( 2 ) ( 106.51 ) } { ( 20 ) } } \rightarrow \sqrt { \frac { 213.02 } { 20 } } \rightarrow \sqrt { 10.65 }$$

Evaluate

$$\frac{\sqrt{106510}}{100}\approx 3.263586984$$

Solution Steps

Multiply 2 and 106.51 to get 213.02.

$$\sqrt{\frac{213.02}{20}}$$

Expand \frac{213.02}{20} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{21302}{2000}}$$

Reduce the fraction \frac{21302}{2000} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{10651}{1000}}$$

Rewrite the square root of the division \sqrt{\frac{10651}{1000}} as the division of square roots \frac{\sqrt{10651}}{\sqrt{1000}}.

$$\frac{\sqrt{10651}}{\sqrt{1000}}$$

Factor 1000=10^{2}\times 10. Rewrite the square root of the product \sqrt{10^{2}\times 10} as the product of square roots \sqrt{10^{2}}\sqrt{10}. Take the square root of 10^{2}.

$$\frac{\sqrt{10651}}{10\sqrt{10}}$$

Rationalize the denominator of \frac{\sqrt{10651}}{10\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{\sqrt{10651}\sqrt{10}}{10\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{\sqrt{10651}\sqrt{10}}{10\times 10}$$

To multiply \sqrt{10651} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{\sqrt{106510}}{10\times 10}$$

Multiply 10 and 10 to get 100.

$$\frac{\sqrt{106510}}{100}$$