Solve frac{sqrt{12}*sqrt{6}}{sqrt{3}}

$$\frac{ \sqrt{ 12 } \times \sqrt{ 6 } }{ \sqrt{ 3 } }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Factor 12=6\times 2. Rewrite the square root of the product \sqrt{6\times 2} as the product of square roots \sqrt{6}\sqrt{2}.

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

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

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

Rationalize the denominator of \frac{6\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

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

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

$$2\sqrt{6}$$