Solve -12sqrt{11}*sqrt{1/11}

$$- 12 \sqrt { 11 } \times \sqrt { \frac { 1 } { 11 } }$$

Evaluate

$$-12$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{11}} as the division of square roots \frac{\sqrt{1}}{\sqrt{11}}.

$$-12\sqrt{11}\times \frac{\sqrt{1}}{\sqrt{11}}$$

Calculate the square root of 1 and get 1.

$$-12\sqrt{11}\times \frac{1}{\sqrt{11}}$$

Rationalize the denominator of \frac{1}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$-12\sqrt{11}\times \frac{\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$-12\sqrt{11}\times \frac{\sqrt{11}}{11}$$

Express -12\times \frac{\sqrt{11}}{11} as a single fraction.

$$\frac{-12\sqrt{11}}{11}\sqrt{11}$$

Express \frac{-12\sqrt{11}}{11}\sqrt{11} as a single fraction.

$$\frac{-12\sqrt{11}\sqrt{11}}{11}$$

Multiply \sqrt{11} and \sqrt{11} to get 11.

$$\frac{-12\times 11}{11}$$

Cancel out 11 and 11.

$$-12$$

Factor

$$-12$$