Solve 1/2*sqrt{3/2}+sqrt{3/2}*1/2

$$\frac{ 1 }{ 2 } \times \sqrt{ \frac{ 3 }{ 2 } } + \sqrt{ \frac{ 3 }{ 2 } } \times \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{\sqrt{6}}{2}\approx 1.224744871$$

Solution Steps

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

$$\frac{1}{2}\times \frac{\sqrt{3}}{\sqrt{2}}+\sqrt{\frac{3}{2}}\times \frac{1}{2}$$

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

$$\frac{1}{2}\times \frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\sqrt{\frac{3}{2}}\times \frac{1}{2}$$

The square of \sqrt{2} is 2.

$$\frac{1}{2}\times \frac{\sqrt{3}\sqrt{2}}{2}+\sqrt{\frac{3}{2}}\times \frac{1}{2}$$

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

$$\frac{1}{2}\times \frac{\sqrt{6}}{2}+\sqrt{\frac{3}{2}}\times \frac{1}{2}$$

Multiply \frac{1}{2} times \frac{\sqrt{6}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{6}}{2\times 2}+\sqrt{\frac{3}{2}}\times \frac{1}{2}$$

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

$$\frac{\sqrt{6}}{2\times 2}+\frac{\sqrt{3}}{\sqrt{2}}\times \frac{1}{2}$$

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

$$\frac{\sqrt{6}}{2\times 2}+\frac{\sqrt{3}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{1}{2}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{6}}{2\times 2}+\frac{\sqrt{3}\sqrt{2}}{2}\times \frac{1}{2}$$

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

$$\frac{\sqrt{6}}{2\times 2}+\frac{\sqrt{6}}{2}\times \frac{1}{2}$$

Multiply \frac{\sqrt{6}}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Multiply 2 and 2 to get 4.

$$2\times \frac{\sqrt{6}}{4}$$

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

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