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

$$2 \sqrt { 6 } \cdot 3 \sqrt { 2 } - 2 \sqrt { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{34\sqrt{3}}{3}\approx 19.629909152$$

Short Solution Steps

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

Multiply \sqrt{2} and \sqrt{2} to get 2.

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

Multiply 2 and 3 to get 6.

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

Multiply 6 and 2 to get 12.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

Express -2\times \frac{\sqrt{3}}{3} as a single fraction.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 12\sqrt{3} times \frac{3}{3}.

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

Since \frac{3\times 12\sqrt{3}}{3} and \frac{-2\sqrt{3}}{3} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3\times 12\sqrt{3}-2\sqrt{3}.

$$\frac{36\sqrt{3}-2\sqrt{3}}{3}$$

Do the calculations in 36\sqrt{3}-2\sqrt{3}.

$$\frac{34\sqrt{3}}{3}$$