Solve (sqrt{32}-sqrt{2})sqrt{2}

$$( \sqrt { 32 } - \sqrt { 2 } ) \sqrt { 2 }$$

Evaluate

$$6$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\left(4\sqrt{2}-\sqrt{2}\right)\sqrt{2}$$

Combine 4\sqrt{2} and -\sqrt{2} to get 3\sqrt{2}.

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

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

$$3\times 2$$

Multiply 3 and 2 to get 6.

$$6$$

Factor

$$2\times 3$$