Solve 4sqrt{1/2}div(-sqrt{6})*1/3sqrt{12}

$$4 \sqrt { \frac { 1 } { 2 } } \div ( - \sqrt { 6 } ) \times \frac { 1 } { 3 } \sqrt { 12 }$$

Evaluate

$$-\frac{4}{3}\approx -1.333333333$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\frac{4\times \frac{\sqrt{1}}{\sqrt{2}}}{-\sqrt{6}}\times \frac{1}{3}\sqrt{12}$$

Calculate the square root of 1 and get 1.

$$\frac{4\times \frac{1}{\sqrt{2}}}{-\sqrt{6}}\times \frac{1}{3}\sqrt{12}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{-\sqrt{6}}\times \frac{1}{3}\sqrt{12}$$

The square of \sqrt{2} is 2.

$$\frac{4\times \frac{\sqrt{2}}{2}}{-\sqrt{6}}\times \frac{1}{3}\sqrt{12}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$\frac{2\sqrt{2}}{-\sqrt{6}}\times \frac{1}{3}\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

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

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

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

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

Express \frac{2\sqrt{2}\times 2}{\left(-\sqrt{6}\right)\times 3}\sqrt{3} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{2}\sqrt{3}}{\left(-\sqrt{6}\right)\times 3}$$

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

$$\frac{4\sqrt{6}}{\left(-\sqrt{6}\right)\times 3}$$

Extract the negative sign in \sqrt{6}.

$$\frac{-\left(-1\right)\times 4\sqrt{6}}{-3\sqrt{6}}$$

Cancel out -\sqrt{6} in both numerator and denominator.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Factor

$$-\frac{4}{3} = -1\frac{1}{3} = -1.3333333333333333$$