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

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

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

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

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

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

Calculate the square root of 4 and get 2.

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

Multiply 3 and 2 to get 6.

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

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

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

The square of \sqrt{6} is 6.

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

Cancel out 6 and 6.

$$\sqrt{6}$$