Solve 2sqrt{32}+3sqrt{8}-4sqrt{18}-2=

$$2 \sqrt { 32 } + 3 \sqrt { 8 } - 4 \sqrt { 18 } - 2 =$$

Evaluate

$$2\sqrt{2}-2\approx 0.828427125$$

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}.

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

Multiply 2 and 4 to get 8.

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

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}.

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

Multiply 3 and 2 to get 6.

$$8\sqrt{2}+6\sqrt{2}-4\sqrt{18}-2$$

Combine 8\sqrt{2} and 6\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}-4\sqrt{18}-2$$

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}.

$$14\sqrt{2}-4\times 3\sqrt{2}-2$$

Multiply -4 and 3 to get -12.

$$14\sqrt{2}-12\sqrt{2}-2$$

Combine 14\sqrt{2} and -12\sqrt{2} to get 2\sqrt{2}.

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