Solve 6sqrt{7/2}

$$6 \sqrt { \frac { 7 } { 2 } }$$

Evaluate

$$3\sqrt{14}\approx 11.22497216$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{2}} as the division of square roots \frac{\sqrt{7}}{\sqrt{2}}.

$$6\times \frac{\sqrt{7}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$6\times \frac{\sqrt{7}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$6\times \frac{\sqrt{7}\sqrt{2}}{2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$6\times \frac{\sqrt{14}}{2}$$

Cancel out 2, the greatest common factor in 6 and 2.

$$3\sqrt{14}$$