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2\sqrt{2}-\sqrt{32}+\sqrt{128}
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}.
2\sqrt{2}-4\sqrt{2}+\sqrt{128}
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\sqrt{2}+\sqrt{128}
Combine 2\sqrt{2} and -4\sqrt{2} to get -2\sqrt{2}.
-2\sqrt{2}+8\sqrt{2}
Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.
6\sqrt{2}
Combine -2\sqrt{2} and 8\sqrt{2} to get 6\sqrt{2}.