Question

what smallest number should 7803 be multiplied with so that the product become a perfect cube.​

Answer 1

Answer:

Question:

what smallest number should 7803 be multiplied with so that the product become a perfect cube.

Solution:

on factorising 7803 into prime factors, we get

$7803 = 3 \times 3 \times 3 \times 17 \times 17$

on grouping the factors in triples of equal factors, we get

7803 = {3 × 3 × 3 } 17 × 17

it is evident that the prime factors of 7803 cannot be grouped into triples of equal factors such as no factor is left over. therefore, 7803 is is not perfect cube. however, if if the number is multiplied by 17, the factors can be grouped into triples of equal factors such that no factor is left over.

$\: \: \: \: \: \mapsto \sf thus, \: 7803 \: should \: be \: multiplied \\ \sf by \: 17 \: \: to \: make \: it \: a \: perfect \: cube$

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