Solve {l}{sqrt{32}+5sqrt{2}-sqrt{200}+}{+sqrt{2}}

$$\left. \begin{array} { l } { \sqrt { 32 } + 5 \sqrt { 2 } - \sqrt { 200 } + } \\ { + \sqrt { 2 } } \end{array} \right.$$

Evaluate

$$0$$

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}.

$$4\sqrt{2}+5\sqrt{2}-\sqrt{200}+\sqrt{2}$$

Combine 4\sqrt{2} and 5\sqrt{2} to get 9\sqrt{2}.

$$9\sqrt{2}-\sqrt{200}+\sqrt{2}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$9\sqrt{2}-10\sqrt{2}+\sqrt{2}$$

Combine 9\sqrt{2} and -10\sqrt{2} to get -\sqrt{2}.

$$-\sqrt{2}+\sqrt{2}$$

Combine -\sqrt{2} and \sqrt{2} to get 0.

$$0$$

Factor

$$0$$