Solve sqrt{12}div(3sqrt{1/3}-2sqrt{3})sqrt{12}

$$\sqrt { 12 } \div ( 3 \sqrt { \frac { 1 } { 3 } } - 2 \sqrt { 3 } ) \sqrt { 12 }$$

Evaluate

$$-4\sqrt{3}\approx -6.92820323$$

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}.

$$\frac{2\sqrt{3}}{3\sqrt{\frac{1}{3}}-2\sqrt{3}}\sqrt{12}$$

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

$$\frac{2\sqrt{3}}{3\times \frac{\sqrt{1}}{\sqrt{3}}-2\sqrt{3}}\sqrt{12}$$

Calculate the square root of 1 and get 1.

$$\frac{2\sqrt{3}}{3\times \frac{1}{\sqrt{3}}-2\sqrt{3}}\sqrt{12}$$

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

$$\frac{2\sqrt{3}}{3\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-2\sqrt{3}}\sqrt{12}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{3\times \frac{\sqrt{3}}{3}-2\sqrt{3}}\sqrt{12}$$

Cancel out 3 and 3.

$$\frac{2\sqrt{3}}{\sqrt{3}-2\sqrt{3}}\sqrt{12}$$

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

$$\frac{2\sqrt{3}}{-\sqrt{3}}\sqrt{12}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{2}{-1}\sqrt{12}$$

Fraction \frac{2}{-1} can be rewritten as -2 by extracting the negative sign.

$$-2\sqrt{12}$$

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}.

$$-2\times 2\sqrt{3}$$

Multiply -2 and 2 to get -4.

$$-4\sqrt{3}$$