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

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

Evaluate

$$2\sqrt{3}-\sqrt{6}\approx 1.014611872$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

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

$$\frac{2\sqrt{6}\left(\sqrt{2}-1\right)}{2}$$

Cancel out 2 and 2.

$$\sqrt{6}\left(\sqrt{2}-1\right)$$

Use the distributive property to multiply \sqrt{6} by \sqrt{2}-1.

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

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}.

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

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

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