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0+\sqrt{32}
Anything times zero gives zero.
0+4\sqrt{2}
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}
Anything plus zero gives itself.