Solve 2sqrt{12}*sqrt{1/6}

$$2 \sqrt { 12 } \times \sqrt { \frac { 1 } { 6 } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{3}\sqrt{\frac{1}{6}}$$

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

$$4\sqrt{3}\times \frac{\sqrt{1}}{\sqrt{6}}$$

Calculate the square root of 1 and get 1.

$$4\sqrt{3}\times \frac{1}{\sqrt{6}}$$

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

$$4\sqrt{3}\times \frac{\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$4\sqrt{3}\times \frac{\sqrt{6}}{6}$$

Express 4\times \frac{\sqrt{6}}{6} as a single fraction.

$$\frac{4\sqrt{6}}{6}\sqrt{3}$$

Divide 4\sqrt{6} by 6 to get \frac{2}{3}\sqrt{6}.

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{2}{3}\sqrt{3}\sqrt{2}\sqrt{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{2}{3}\times 3\sqrt{2}$$

Cancel out 3 and 3.

$$2\sqrt{2}$$