Solve sqrt{2}(sqrt{18}+sqrt{8})

$$\sqrt { 2 } ( \sqrt { 18 } + \sqrt { 8 } )$$

Evaluate

$$10$$

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}.

$$\sqrt{2}\left(3\sqrt{2}+\sqrt{8}\right)$$

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}.

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

Combine 3\sqrt{2} and 2\sqrt{2} to get 5\sqrt{2}.

$$\sqrt{2}\times 5\sqrt{2}$$

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

$$2\times 5$$

Multiply 2 and 5 to get 10.

$$10$$

Factor

$$2\times 5$$