Solve sqrt{38/22}

$$\sqrt{ \frac{ 38 }{ 22 } }$$

Evaluate

$$\frac{\sqrt{209}}{11}\approx 1.314257481$$

Solution Steps

Reduce the fraction \frac{38}{22} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{19}{11}}$$

Rewrite the square root of the division \sqrt{\frac{19}{11}} as the division of square roots \frac{\sqrt{19}}{\sqrt{11}}.

$$\frac{\sqrt{19}}{\sqrt{11}}$$

Rationalize the denominator of \frac{\sqrt{19}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\sqrt{19}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{\sqrt{19}\sqrt{11}}{11}$$

To multiply \sqrt{19} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{209}}{11}$$