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

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

Evaluate

$$-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 in both numerator and denominator.

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

Multiply \frac{-\sqrt{2}}{2} times \frac{\sqrt{6}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 3 to get 6.

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

Divide -2\sqrt{3} by 6 to get -\frac{1}{3}\sqrt{3}.

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