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

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

Evaluate

$$-\frac{2\sqrt{3}}{3}+2\sqrt{2}-2\approx -0.326273414$$

Solution Steps

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

$$2\sqrt{2}-\frac{1}{3}\sqrt{6}\sqrt{2}-2$$

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}.

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

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

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

Multiply \frac{1}{3} and 2 to get \frac{2}{3}.

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

Factor

$$\frac{2 {(3 \sqrt{2} - \sqrt{3} - 3)}}{3} = -0.326273413633061$$