Solve 5sqrt{3/2}

$$5 \sqrt { \frac { 3 } { 2 } }$$

Evaluate

$$\frac{5\sqrt{6}}{2}\approx 6.123724357$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

$$5\times \frac{\sqrt{3}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$5\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$5\times \frac{\sqrt{3}\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$5\times \frac{\sqrt{6}}{2}$$

Express 5\times \frac{\sqrt{6}}{2} as a single fraction.

$$\frac{5\sqrt{6}}{2}$$