Express ${56}$ as a product of its prime factors.[1] Use prime factors to explain why \({14 \times

Question

Express ${56}$ as a product of its prime factors.[1] Use prime factors to explain why ${14 \times 56}$ is a perfect square.[2] The number ${14k}$ is a perfect cube. Find the smallest positive integer value of ${k}$.[1]

Accepted Answer

(a) $56=2^3\times7$. (b) $14\times56=2^4\times7^2$, so it is a perfect square. (c) $k=196$.

2023 AISS EM S1 EOY P1 Q10

2023 AISS EM S1 EOY P1 Q10

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