Solve sqrt{66/10}

$$\sqrt{ \frac{ 66 }{ 10 } }$$

Evaluate

$$\frac{\sqrt{165}}{5}\approx 2.569046516$$

Solution Steps

Reduce the fraction \frac{66}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{33}{5}}$$

Rewrite the square root of the division \sqrt{\frac{33}{5}} as the division of square roots \frac{\sqrt{33}}{\sqrt{5}}.

$$\frac{\sqrt{33}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{33}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{33}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{33}\sqrt{5}}{5}$$

To multiply \sqrt{33} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{165}}{5}$$