Solve sqrt{51/99}

$$\sqrt{ \frac{ 51 }{ 99 } }$$

Evaluate

$$\frac{\sqrt{561}}{33}\approx 0.717740563$$

Solution Steps

Reduce the fraction \frac{51}{99} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{17}{33}}$$

Rewrite the square root of the division \sqrt{\frac{17}{33}} as the division of square roots \frac{\sqrt{17}}{\sqrt{33}}.

$$\frac{\sqrt{17}}{\sqrt{33}}$$

Rationalize the denominator of \frac{\sqrt{17}}{\sqrt{33}} by multiplying numerator and denominator by \sqrt{33}.

$$\frac{\sqrt{17}\sqrt{33}}{\left(\sqrt{33}\right)^{2}}$$

The square of \sqrt{33} is 33.

$$\frac{\sqrt{17}\sqrt{33}}{33}$$

To multiply \sqrt{17} and \sqrt{33}, multiply the numbers under the square root.

$$\frac{\sqrt{561}}{33}$$