Question

what is the smallest number that should be multiplied by 36864 to make it a perfect cube
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Answer 1

Answer:

3 is your answer

Step-by-step explanation:

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Answer 2

To find:

• What is the smallest number that should be multiplied by 36864 to make it a perfect cube?

Solution :

$\sf \: Prime \: Factorization \: of \: 36864 \\ = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\ \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \\ = (2 \times 2 \times 2) \times (2 \times 2 \times 2) \\ \times (2 \times 2 \times 2) \times (2 \times 2 \times 2) \\ \times (3 \times 3) \\ \sf \: for \: a \: number \: to \: be \: perfect \: cube \\ \sf each \: of \: its \: prime \: factor \: should \: be \: present \: \\ \sf \: in \: triplet \\ \sf \: so \: 36864 \: should \:be \: multipies \: \\ \sf \: with \: 3 \: to \: make \: its \: perfect \: \sf\\ cube.$