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$a+b+c$
The expression simplifies to \(2 \sqrt[3]{12}\), so the answer is 2 + 3 + 12 = 17.
+2666 \(\sqrt[3]{250} = 5 \sqrt[3]{2}\)
\(\sqrt[3]{54} = 3\sqrt[3]2\)
\(5\sqrt[3]{2} + 3\sqrt[3]{2} = 8\sqrt[3]{2}\)
\(\sqrt[3]{8\sqrt[3]{2}} = \sqrt[3]{8} \times \sqrt[3]{ \sqrt[3]{2}} = 2\sqrt[9]{2}\)
\(2 + 9 + 2 = \color{brown}\boxed{13}\)
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