Evaluate
10\sqrt{7}-5\sqrt[5]{2}-2\approx 18.714021336
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7\sqrt{7}-\sqrt[5]{32}+3\sqrt{7}-5\sqrt[5]{2}
Factor 343=7^{2}\times 7. Rewrite the square root of the product \sqrt{7^{2}\times 7} as the product of square roots \sqrt{7^{2}}\sqrt{7}. Take the square root of 7^{2}.
7\sqrt{7}-2+3\sqrt{7}-5\sqrt[5]{2}
Calculate \sqrt[5]{32} and get 2.
10\sqrt{7}-2-5\sqrt[5]{2}
Combine 7\sqrt{7} and 3\sqrt{7} to get 10\sqrt{7}.
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