Solve 3/sqrt{3}(2/sqrt{3}-frac{sqrt{12}}{6})

$$\frac { 3 } { \sqrt { 3 } } ( \frac { 2 } { \sqrt { 3 } } - \frac { \sqrt { 12 } } { 6 } )$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{3\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\left(\frac{2}{\sqrt{3}}-\frac{\sqrt{12}}{6}\right)$$

The square of \sqrt{3} is 3.

$$\frac{3\sqrt{3}}{3}\left(\frac{2}{\sqrt{3}}-\frac{\sqrt{12}}{6}\right)$$

Cancel out 3 and 3.

$$\sqrt{3}\left(\frac{2}{\sqrt{3}}-\frac{\sqrt{12}}{6}\right)$$

Rationalize the denominator of \frac{2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\sqrt{3}\left(\frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-\frac{\sqrt{12}}{6}\right)$$

The square of \sqrt{3} is 3.

$$\sqrt{3}\left(\frac{2\sqrt{3}}{3}-\frac{\sqrt{12}}{6}\right)$$

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}.

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

Divide 2\sqrt{3} by 6 to get \frac{1}{3}\sqrt{3}.

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

Use the distributive property to multiply \sqrt{3} by \frac{2\sqrt{3}}{3}-\frac{1}{3}\sqrt{3}.

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

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

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

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

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

Cancel out 3 and 3.

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

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

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

Multiply 3 and -1 to get -3.

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

Multiply -3 times \frac{1}{3}.

$$2-1$$

Subtract 1 from 2 to get 1.

$$1$$

Factor

$$1$$