Solve frac{sqrt{2}}{2}*2*(sqrt{2}-sqrt{6})

$$\frac{ \sqrt{ 2 } }{ 2 } \times 2 \times ( \sqrt{ 2 } - \sqrt{ 6 } )$$

Evaluate

$$2-2\sqrt{3}\approx -1.464101615$$

Solution Steps

Cancel out 2 and 2.

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

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

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

The square of \sqrt{2} is 2.

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

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}.

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

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

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