Solve sqrt{748/120}

$$\sqrt{ \frac{ 748 }{ 120 } }$$

Evaluate

$$\frac{\sqrt{5610}}{30}\approx 2.496664441$$

Solution Steps

Reduce the fraction \frac{748}{120} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{187}{30}}$$

Rewrite the square root of the division \sqrt{\frac{187}{30}} as the division of square roots \frac{\sqrt{187}}{\sqrt{30}}.

$$\frac{\sqrt{187}}{\sqrt{30}}$$

Rationalize the denominator of \frac{\sqrt{187}}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$\frac{\sqrt{187}\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$\frac{\sqrt{187}\sqrt{30}}{30}$$

To multiply \sqrt{187} and \sqrt{30}, multiply the numbers under the square root.

$$\frac{\sqrt{5610}}{30}$$