Solve 3/sqrt{3}-sqrt{1/3}

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

Evaluate

$$\frac{2\sqrt{3}}{3}\approx 1.154700538$$

Short Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Cancel out 3 and 3.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Since \frac{3\sqrt{3}}{3} and \frac{\sqrt{3}}{3} have the same denominator, subtract them by subtracting their numerators.

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

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

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