Competition problem — Number theory

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Number theory Difficulty 2.5 Junior Find the answer

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

Pick one

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 $\boxed{ \text{(D)}}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.