Solve sqrt{3/2}+sqrt{3/2}

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

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

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

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

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

$$\frac{\sqrt{6}}{2}+\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

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

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

Combine \frac{\sqrt{6}}{2} and \frac{\sqrt{6}}{2} to get \sqrt{6}.

$$\sqrt{6}$$