Solve 4sqrt{5/2}

$$4 \sqrt{ \frac{ 5 }{ 2 } }$$

Evaluate

$$2\sqrt{10}\approx 6.32455532$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$4\times \frac{\sqrt{5}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\times \frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$4\times \frac{\sqrt{5}\sqrt{2}}{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$4\times \frac{\sqrt{10}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{10}$$