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2\sqrt{5}-\sqrt[3]{16}+\sqrt[3]{250}-\sqrt{5}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
\sqrt{5}-\sqrt[3]{16}+\sqrt[3]{250}
Combine 2\sqrt{5} and -\sqrt{5} to get \sqrt{5}.