Solve (2sqrt{3}-3sqrt{1/3})*sqrt{6}

$$(2 \sqrt{ 3 } -3 \sqrt{ \frac{ 1 }{ 3 } } ) \times \sqrt{ 6 }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

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

$$\left(2\sqrt{3}-3\times \frac{\sqrt{1}}{\sqrt{3}}\right)\sqrt{6}$$

Calculate the square root of 1 and get 1.

$$\left(2\sqrt{3}-3\times \frac{1}{\sqrt{3}}\right)\sqrt{6}$$

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

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

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

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

Combine 2\sqrt{3} and -\sqrt{3} to get \sqrt{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}.

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

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

$$3\sqrt{2}$$