Solve 2sqrt{3/2}-sqrt{2/}

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

Evaluate

$$\sqrt{6}-\sqrt{2}\approx 1.03527618$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Cancel out 2 and 2.

$$\sqrt{6}-\sqrt{\frac{2}{1}}$$

Anything divided by one gives itself.

$$\sqrt{6}-\sqrt{2}$$

Factor

$$\sqrt{6} - \sqrt{2} = 1.03527618$$