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, 2006

Number theory Difficulty 2.0 Junior Find the answer Canada

What is the smallest positive integer $p$ for which $\sqrt{2^3 \times 5 \times p}$ is an integer?

(A) $2$ (B) $5$ (C) $10$ (D) $1$ (E) $20$

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.