Solve sqrt{11/2}div(-1/2sqrt{1/6})

$$\sqrt { 1 \frac { 1 } { 2 } } \div ( - \frac { 1 } { 2 } \sqrt { \frac { 1 } { 6 } } )$$

Evaluate

$$-6$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

Rewrite the square root of the division \sqrt{\frac{3}{2}} as the division of square roots \frac{\sqrt{3}}{\sqrt{2}}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Rewrite the square root of the division \sqrt{\frac{1}{6}} as the division of square roots \frac{\sqrt{1}}{\sqrt{6}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

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

The square of \sqrt{6} is 6.

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

Multiply -\frac{1}{2} times \frac{\sqrt{6}}{6} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{\sqrt{6}\times 2\times 6}{2\left(-1\right)\sqrt{6}}$$

Cancel out 2\sqrt{6} in both numerator and denominator.

$$\frac{6}{-1}$$

Fraction \frac{6}{-1} can be rewritten as -6 by extracting the negative sign.

$$-6$$

Factor

$$-6$$