Solve sqrt{2}(sqrt{8}+sqrt{2})

$$\sqrt { 2 } ( \sqrt { 8 } + \sqrt { 2 } )$$

Evaluate

$$6$$

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 3\sqrt{2}.

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

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

$$2\times 3$$

Multiply 2 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$