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

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

Evaluate

$$-\frac{5\sqrt{2}}{3}\approx -2.357022604$$

Solution Steps

Since -\frac{2}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from -2 to get -4.

$$\frac{-\frac{4}{3}-2}{\sqrt{2}}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{-\frac{4}{3}-\frac{6}{3}}{\sqrt{2}}$$

Since -\frac{4}{3} and \frac{6}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-4-6}{3}}{\sqrt{2}}$$

Subtract 6 from -4 to get -10.

$$\frac{-\frac{10}{3}}{\sqrt{2}}$$

Express \frac{-\frac{10}{3}}{\sqrt{2}} as a single fraction.

$$\frac{-10}{3\sqrt{2}}$$

Rationalize the denominator of \frac{-10}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-10\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-10\sqrt{2}}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-5\sqrt{2}}{3}$$