Solve 2/sqrt{3}-sqrt{2}

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

Evaluate

$$\frac{\sqrt{2}\left(\sqrt{6}-3\right)}{3}\approx -0.259513024$$

Short Solution Steps

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

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

The square of \sqrt{3} is 3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2} times \frac{3}{3}.

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

Since \frac{2\sqrt{3}}{3} and \frac{3\sqrt{2}}{3} have the same denominator, subtract them by subtracting their numerators.

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

Factor

$$\frac{\sqrt{2} {(\sqrt{2} \sqrt{3} - 3)}}{3} = -0.2595130239938434$$