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

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

Evaluate

$$0$$

Solution Steps

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

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Cancel out 2 and 2.

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

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Cancel out 3 and 3.

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

Combine \sqrt{6} and -\sqrt{6} to get 0.

$$0$$

Factor

$$0$$