Solve sqrt{2/3}-sqrt{6}

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

Evaluate

$$-\frac{2\sqrt{6}}{3}\approx -1.632993162$$

Solution Steps

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

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Combine \frac{\sqrt{6}}{3} and -\sqrt{6} to get -\frac{2}{3}\sqrt{6}.

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