Solve sqrt{510/4}

$$\sqrt { \frac { 510 } { 4 } }$$

Evaluate

$$\frac{\sqrt{510}}{2}\approx 11.291589791$$

Solution Steps

Reduce the fraction \frac{510}{4} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{255}{2}}$$

Rewrite the square root of the division \sqrt{\frac{255}{2}} as the division of square roots \frac{\sqrt{255}}{\sqrt{2}}.

$$\frac{\sqrt{255}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{255}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{255}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{255}\sqrt{2}}{2}$$

To multiply \sqrt{255} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{510}}{2}$$