Solve sqrt{59458/182}

$$\sqrt{ \frac{ 59458 }{ 182 } }$$

Evaluate

$$\frac{\sqrt{55211}}{13}\approx 18.074631606$$

Solution Steps

Reduce the fraction \frac{59458}{182} to lowest terms by extracting and canceling out 14.

$$\sqrt{\frac{4247}{13}}$$

Rewrite the square root of the division \sqrt{\frac{4247}{13}} as the division of square roots \frac{\sqrt{4247}}{\sqrt{13}}.

$$\frac{\sqrt{4247}}{\sqrt{13}}$$

Rationalize the denominator of \frac{\sqrt{4247}}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{\sqrt{4247}\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{\sqrt{4247}\sqrt{13}}{13}$$

To multiply \sqrt{4247} and \sqrt{13}, multiply the numbers under the square root.

$$\frac{\sqrt{55211}}{13}$$