Solve (-2sqrt{51/2})div(-1/5sqrt{11/18})

$$( - 2 \sqrt { 5 \frac { 1 } { 2 } } ) \div ( - \frac { 1 } { 5 } \sqrt { \frac { 11 } { 18 } } )$$

Evaluate

$$30$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{-2\sqrt{\frac{10+1}{2}}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

Add 10 and 1 to get 11.

$$\frac{-2\sqrt{\frac{11}{2}}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

Rewrite the square root of the division \sqrt{\frac{11}{2}} as the division of square roots \frac{\sqrt{11}}{\sqrt{2}}.

$$\frac{-2\times \frac{\sqrt{11}}{\sqrt{2}}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

Rationalize the denominator of \frac{\sqrt{11}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-2\times \frac{\sqrt{11}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

The square of \sqrt{2} is 2.

$$\frac{-2\times \frac{\sqrt{11}\sqrt{2}}{2}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{-2\times \frac{\sqrt{22}}{2}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

Cancel out 2 and 2.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\sqrt{\frac{11}{18}}}$$

Rewrite the square root of the division \sqrt{\frac{11}{18}} as the division of square roots \frac{\sqrt{11}}{\sqrt{18}}.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\times \frac{\sqrt{11}}{\sqrt{18}}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\times \frac{\sqrt{11}}{3\sqrt{2}}}$$

Rationalize the denominator of \frac{\sqrt{11}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\times \frac{\sqrt{11}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\times \frac{\sqrt{11}\sqrt{2}}{3\times 2}}$$

To multiply \sqrt{11} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\times \frac{\sqrt{22}}{3\times 2}}$$

Multiply 3 and 2 to get 6.

$$\frac{-\sqrt{22}}{-\frac{1}{5}\times \frac{\sqrt{22}}{6}}$$

Multiply -\frac{1}{5} times \frac{\sqrt{22}}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\sqrt{22}}{\frac{-\sqrt{22}}{5\times 6}}$$

Divide -\sqrt{22} by \frac{-\sqrt{22}}{5\times 6} by multiplying -\sqrt{22} by the reciprocal of \frac{-\sqrt{22}}{5\times 6}.

$$\frac{-\sqrt{22}\times 5\times 6}{-\sqrt{22}}$$

Cancel out -\sqrt{22} in both numerator and denominator.

$$5\times 6$$

Multiply 5 and 6 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$