Solve sqrt{27.6/9}

$$\sqrt { \frac { 27.6 } { 9 } }$$

Evaluate

$$\frac{\sqrt{690}}{15}\approx 1.751190072$$

Solution Steps

Expand \frac{27.6}{9} by multiplying both numerator and the denominator by 10.

$$\sqrt{\frac{276}{90}}$$

Reduce the fraction \frac{276}{90} to lowest terms by extracting and canceling out 6.

$$\sqrt{\frac{46}{15}}$$

Rewrite the square root of the division \sqrt{\frac{46}{15}} as the division of square roots \frac{\sqrt{46}}{\sqrt{15}}.

$$\frac{\sqrt{46}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{46}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{46}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{46}\sqrt{15}}{15}$$

To multiply \sqrt{46} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{690}}{15}$$