Solve 2sqrt{6}*4sqrt{1/12}

$$2 \sqrt { 6 } \times 4 \sqrt { \frac { 1 } { 12 } }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Multiply 2 and 4 to get 8.

$$8\sqrt{6}\sqrt{\frac{1}{12}}$$

Rewrite the square root of the division \sqrt{\frac{1}{12}} as the division of square roots \frac{\sqrt{1}}{\sqrt{12}}.

$$8\sqrt{6}\times \frac{\sqrt{1}}{\sqrt{12}}$$

Calculate the square root of 1 and get 1.

$$8\sqrt{6}\times \frac{1}{\sqrt{12}}$$

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}.

$$8\sqrt{6}\times \frac{1}{2\sqrt{3}}$$

Rationalize the denominator of \frac{1}{2\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$8\sqrt{6}\times \frac{\sqrt{3}}{2\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$8\sqrt{6}\times \frac{\sqrt{3}}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$8\sqrt{6}\times \frac{\sqrt{3}}{6}$$

Express 8\times \frac{\sqrt{3}}{6} as a single fraction.

$$\frac{8\sqrt{3}}{6}\sqrt{6}$$

Divide 8\sqrt{3} by 6 to get \frac{4}{3}\sqrt{3}.

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

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}.

$$\frac{4}{3}\sqrt{3}\sqrt{3}\sqrt{2}$$

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

$$\frac{4}{3}\times 3\sqrt{2}$$

Cancel out 3 and 3.

$$4\sqrt{2}$$