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In simplified form, we can write $\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$ as $a\sqrt[b]{c}$ wherea a, b c and are all positive integers. What is$a+b+c$

 Jan 31, 2023
 #1
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The expression simplifies to \(2 \sqrt[3]{12}\), so the answer is 2 + 3 + 12 = 17.

 Jan 31, 2023
 #2
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\(\sqrt[3]{250} = 5 \sqrt[3]{2}\)

\(\sqrt[3]{54} = 3\sqrt[3]2\)

\(5\sqrt[3]{2} + 3\sqrt[3]{2} = 8\sqrt[3]{2}\)

\(\sqrt[3]{8\sqrt[3]{2}} = \sqrt[3]{8} \times \sqrt[3]{ \sqrt[3]{2}} = 2\sqrt[9]{2}\)

\(2 + 9 + 2 = \color{brown}\boxed{13}\)

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 Jan 31, 2023

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