Solve sqrt{11}*sqrt{2}div1/sqrt{6}

$$\sqrt{ 11 } \times \sqrt{ 2 } \div \frac{ 1 }{ \sqrt{ 6 } }$$

Evaluate

$$2\sqrt{33}\approx 11.489125293$$

Solution Steps

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

$$\frac{\sqrt{22}}{\frac{1}{\sqrt{6}}}$$

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

$$\frac{\sqrt{22}}{\frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{22}}{\frac{\sqrt{6}}{6}}$$

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

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

Rationalize the denominator of \frac{\sqrt{22}\times 6}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{22}\times 6\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

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

To multiply \sqrt{22} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{132}\times 6}{6}$$

Cancel out 6 and 6.

$$\sqrt{132}$$

Factor 132=2^{2}\times 33. Rewrite the square root of the product \sqrt{2^{2}\times 33} as the product of square roots \sqrt{2^{2}}\sqrt{33}. Take the square root of 2^{2}.

$$2\sqrt{33}$$