Solve 3sqrt{12}*sqrt{1/3}

$$3 \sqrt{ 12 } \times \sqrt{ \frac{ 1 }{ 3 } }$$

Evaluate

$$6$$

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}.

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

Multiply 3 and 2 to get 6.

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

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Cancel out 3, the greatest common factor in 6 and 3.

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

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

$$2\times 3$$

Multiply 2 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$