Solve sqrt{2}left(sqrt{8}-sqrt{2}right)

$$\sqrt{ 2 } \left( \sqrt{ 8 } - \sqrt{ 2 } \right)$$

Evaluate

$$2$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

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

Combine 2\sqrt{2} and -\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}\sqrt{2}$$

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

$$2$$

Factor

$$2$$