Solve sqrt{9/42}

$$\sqrt { \frac { 9 } { 42 } }$$

Evaluate

$$\frac{\sqrt{42}}{14}\approx 0.46291005$$

Solution Steps

Reduce the fraction \frac{9}{42} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{3}{14}}$$

Rewrite the square root of the division \sqrt{\frac{3}{14}} as the division of square roots \frac{\sqrt{3}}{\sqrt{14}}.

$$\frac{\sqrt{3}}{\sqrt{14}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{3}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{3}\sqrt{14}}{14}$$

To multiply \sqrt{3} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{14}$$