Solve sqrt{2*31/217}

$$\sqrt { \frac { 2 \times 31 } { 217 } }$$

Evaluate

$$\frac{\sqrt{14}}{7}\approx 0.534522484$$

Solution Steps

Multiply 2 and 31 to get 62.

$$\sqrt{\frac{62}{217}}$$

Reduce the fraction \frac{62}{217} to lowest terms by extracting and canceling out 31.

$$\sqrt{\frac{2}{7}}$$

Rewrite the square root of the division \sqrt{\frac{2}{7}} as the division of square roots \frac{\sqrt{2}}{\sqrt{7}}.

$$\frac{\sqrt{2}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{2}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{2}\sqrt{7}}{7}$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{14}}{7}$$