Solve sqrt{32}+2sqrt{8}-3sqrt{18}=

$$\sqrt { 32 } + 2 \sqrt { 8 } - 3 \sqrt { 18 } =$$

Evaluate

$$-\sqrt{2}\approx -1.414213562$$

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}.

$$4\sqrt{2}+2\sqrt{8}-3\sqrt{18}$$

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}.

$$4\sqrt{2}+2\times 2\sqrt{2}-3\sqrt{18}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}+4\sqrt{2}-3\sqrt{18}$$

Combine 4\sqrt{2} and 4\sqrt{2} to get 8\sqrt{2}.

$$8\sqrt{2}-3\sqrt{18}$$

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}.

$$8\sqrt{2}-3\times 3\sqrt{2}$$

Multiply -3 and 3 to get -9.

$$8\sqrt{2}-9\sqrt{2}$$

Combine 8\sqrt{2} and -9\sqrt{2} to get -\sqrt{2}.

$$-\sqrt{2}$$