1990 AHSME Problems/Problem 5

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Problem

Which of these numbers is largest?

$\text{(A) } \sqrt{\sqrt[3]{5\cdot 6}}\quad \text{(B) } \sqrt{6\sqrt[3]{5}}\quad \text{(C) } \sqrt{5\sqrt[3]{6}}\quad \text{(D) } \sqrt[3]{5\sqrt{6}}\quad \text{(E) } \sqrt[3]{6\sqrt{5}}$

Solution

Putting them all in the form $\sqrt{\sqrt[3]N}$ (the order of the radicals doesn't matter), the resulting interior numbers are \[30, 1080, 750, 150, 180\] so the answer is $\fbox{B}$

See also

1990 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
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