Evaluate
5\sqrt{5}-4\sqrt[3]{2}\approx 6.140655688
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2\sqrt{5}-\sqrt[3]{2}+\sqrt{45}-\sqrt[3]{54}
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}.
2\sqrt{5}-\sqrt[3]{2}+3\sqrt{5}-\sqrt[3]{54}
Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.
5\sqrt{5}-\sqrt[3]{2}-\sqrt[3]{54}
Combine 2\sqrt{5} and 3\sqrt{5} to get 5\sqrt{5}.
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