Solve sqrt{2}(4sqrt{2}+sqrt{8})

$$\sqrt { 2 } ( 4 \sqrt { 2 } + \sqrt { 8 } )$$

Evaluate

$$12$$

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}.

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

Combine 4\sqrt{2} and 2\sqrt{2} to get 6\sqrt{2}.

$$\sqrt{2}\times 6\sqrt{2}$$

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

$$2\times 6$$

Multiply 2 and 6 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$