Solve -sqrt{22/3}div(-2/3sqrt{3/4})=

$$- \sqrt { 2 \frac { 2 } { 3 } } \div ( - \frac { 2 } { 3 } \sqrt { \frac { 3 } { 4 } } ) =$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Multiply 2 and 3 to get 6.

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

Add 6 and 2 to get 8.

$$\frac{-\sqrt{\frac{8}{3}}}{-\frac{2}{3}\sqrt{\frac{3}{4}}}$$

Rewrite the square root of the division \sqrt{\frac{8}{3}} as the division of square roots \frac{\sqrt{8}}{\sqrt{3}}.

$$\frac{-\frac{\sqrt{8}}{\sqrt{3}}}{-\frac{2}{3}\sqrt{\frac{3}{4}}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

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

$$\frac{-\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{-\frac{2}{3}\sqrt{\frac{3}{4}}}$$

The square of \sqrt{3} is 3.

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

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

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

Rewrite the square root of the division \sqrt{\frac{3}{4}} as the division of square roots \frac{\sqrt{3}}{\sqrt{4}}.

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

Calculate the square root of 4 and get 2.

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

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

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

Cancel out 2 in both numerator and denominator.

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

Divide -\frac{2\sqrt{6}}{3} by \frac{-\sqrt{3}}{3} by multiplying -\frac{2\sqrt{6}}{3} by the reciprocal of \frac{-\sqrt{3}}{3}.

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

Cancel out 3 and 3.

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

Cancel out -1 in both numerator and denominator.

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

Rationalize the denominator of \frac{2\sqrt{6}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Cancel out 3 and 3.

$$2\sqrt{2}$$