Solve sqrt{23331/22}

$$\sqrt{ \frac{ 23331 }{ 22 } }$$

Evaluate

$$\frac{\sqrt{4242}}{2}\approx 32.565318976$$

Solution Steps

Reduce the fraction \frac{23331}{22} to lowest terms by extracting and canceling out 11.

$$\sqrt{\frac{2121}{2}}$$

Rewrite the square root of the division \sqrt{\frac{2121}{2}} as the division of square roots \frac{\sqrt{2121}}{\sqrt{2}}.

$$\frac{\sqrt{2121}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{2121}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2121}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2121}\sqrt{2}}{2}$$

To multiply \sqrt{2121} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{4242}}{2}$$