Solve (sqrt{2}-2sqrt{3})*1/2sqrt{2}

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

Evaluate

$$1-\sqrt{6}\approx -1.449489743$$

Solution Steps

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

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

Multiply -2 times \frac{1}{2}.

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

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

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

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

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

Cancel out 2 and 2.

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

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

$$1-\sqrt{6}$$