Solve frac{sqrt{6}-sqrt{3}}{sqrt{2}}

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

Evaluate

$$-\frac{\sqrt{6}}{2}+\sqrt{3}\approx 0.507305936$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{6}-\sqrt{3}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Use the distributive property to multiply \sqrt{6}-\sqrt{3} by \sqrt{2}.

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

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}.

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

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

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

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

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