Solve sqrt{2}+sqrt{18}-sqrt{32}

$$\sqrt { 2 } + \sqrt { 18 } - \sqrt { 32 }$$

Evaluate

$$0$$

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}.

$$\sqrt{2}+3\sqrt{2}-\sqrt{32}$$

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

$$4\sqrt{2}-\sqrt{32}$$

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}.

$$4\sqrt{2}-4\sqrt{2}$$

Combine 4\sqrt{2} and -4\sqrt{2} to get 0.

$$0$$

Factor

$$0$$