Question
Write true $(T)$ or false $(F)$ for the following statement: $392$ is a perfect cube.
✓
Answer
On factorising 392 into prime factors,
we got: $392 = 2 \times 2 \times 2 \times 7 \times 7$ On grouping the factors in triples of equal factors,
we get: $392 = \{2 \times 2 \times 2\} \times 7 \times 7$ It is evident that the prime factors of $392$ cannot be grouped into triples of equal factors such that no factor is left over.
Therefore, $392$ is not a perfect cube.
we got: $392 = 2 \times 2 \times 2 \times 7 \times 7$ On grouping the factors in triples of equal factors,
we get: $392 = \{2 \times 2 \times 2\} \times 7 \times 7$ It is evident that the prime factors of $392$ cannot be grouped into triples of equal factors such that no factor is left over.
Therefore, $392$ is not a perfect cube.
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