Solve 4sqrt{12}-6sqrt{1/3}+2=

$$4 \sqrt { 12 } - 6 \sqrt { \frac { 1 } { 3 } } + 2 =$$

Evaluate

$$6\sqrt{3}+2\approx 12.392304845$$

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}.

$$4\times 2\sqrt{3}-6\sqrt{\frac{1}{3}}+2$$

Multiply 4 and 2 to get 8.

$$8\sqrt{3}-6\sqrt{\frac{1}{3}}+2$$

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

$$8\sqrt{3}-6\times \frac{\sqrt{1}}{\sqrt{3}}+2$$

Calculate the square root of 1 and get 1.

$$8\sqrt{3}-6\times \frac{1}{\sqrt{3}}+2$$

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

$$8\sqrt{3}-6\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+2$$

The square of \sqrt{3} is 3.

$$8\sqrt{3}-6\times \frac{\sqrt{3}}{3}+2$$

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

$$8\sqrt{3}-2\sqrt{3}+2$$

Combine 8\sqrt{3} and -2\sqrt{3} to get 6\sqrt{3}.

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

Factor

$$2 {(3 \sqrt{3} + 1)} = 12.392304845$$