1958 AHSME Problems/Problem 8

Problem

Which of these five numbers $\sqrt{\pi^2},\,\sqrt[3]{.8},\,\sqrt[4]{.00016},\,\sqrt[3]{-1}\cdot \sqrt{(.09)^{-1}}$, is (are) rational:

$\textbf{(A)}\ \text{none}\qquad  \textbf{(B)}\ \text{all}\qquad  \textbf{(C)}\ \text{the first and fourth}\qquad  \textbf{(D)}\ \text{only the fourth}\qquad  \textbf{(E)}\ \text{only the first}$

Solution

$\sqrt{\pi^2}=\pi$ is not rational, so eliminate choices $(B)$, $(C)$, and $(E)$. Note that $(-1)^3 = (-1)$, so $\sqrt[3]{-1}=-1$ is rational. We have found one rational number, so we can eliminate choice $(A)$. The answer is $\boxed{ \text{(D)}}$.


See Also

1958 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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