Solve frac{1-sqrt{2}}{sqrt{3}}

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

Evaluate

$$\frac{\sqrt{3}-\sqrt{6}}{3}\approx -0.239146312$$

Solution Steps

Rationalize the denominator of \frac{1-\sqrt{2}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

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

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{3}-\sqrt{6}}{3}$$