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alcumus help

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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