Solve sqrt{24}*sqrt{1/6}

$$\sqrt { 24 } \times \sqrt { \frac { 1 } { 6 } }$$

Evaluate

$$2$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{6} is 6.

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

Cancel out 6, the greatest common factor in 2 and 6.

$$\frac{\sqrt{6}}{3}\sqrt{6}$$

Express \frac{\sqrt{6}}{3}\sqrt{6} as a single fraction.

$$\frac{\sqrt{6}\sqrt{6}}{3}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$