Solve sqrt{6/9})

$$\sqrt{ \frac{ 6 }{ 9 } } )$$

Evaluate

$$\frac{\sqrt{6}}{3}\approx 0.816496581$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{2}{3}}$$

Rewrite the square root of the division \sqrt{\frac{2}{3}} as the division of square roots \frac{\sqrt{2}}{\sqrt{3}}.

$$\frac{\sqrt{2}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

$$\frac{\sqrt{2}\sqrt{3}}{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{6}}{3}$$