Solve left(sqrt{18}-sqrt{2}right)sqrt{2}

$$\left( \sqrt{ 18 } - \sqrt{ 2 } \right) \sqrt{ 2 }$$

Evaluate

$$4$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

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

Combine 3\sqrt{2} and -\sqrt{2} to get 2\sqrt{2}.

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

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

$$2\times 2$$

Multiply 2 and 2 to get 4.

$$4$$

Factor

$$2^{2}$$