Solve 3/2sqrt{3/2}

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

Evaluate

$$\frac{3\sqrt{6}}{4}\approx 1.837117307$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

$$\frac{3}{2}\times \frac{\sqrt{6}}{2}$$

Multiply \frac{3}{2} times \frac{\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{6}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{6}}{4}$$