Question

What is the smallest number by which 4116 must be multiplied so that the product is a perfect cube? In this I have the doubt that when we prime factories 4116 we get 2² and 3¹ then why do we multiply 3×3×2​

Answer 1

Answer:

Answer. so it must be multiplied by one 2 and two 3's. meaning- - 2 × 3 × 3 = 18 answer.

Thus, the required smallest number by which 288 be multiplied to make it a perfect cube i: (2 x 3), i.e. 6.

Answer. so it must be multiplied by one 2 and two 3's. meaning- - 2 × 3 × 3 = 18 answer.

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Answer 2

Given

✭ 4116 is multiplied by a number

✭ Product obtained is a perfect cube

To Find

The number to be multiplied?

Solution

Concept

So we know that for a number to be a perfect cube it needs 3 pairs, exam take the number 27 it has 3×3×3 ...but if it had been 3×3 like in the case of 9 then it can't be a perfect cube

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First we shall find the factors of the given number,

➝ 4116 = 2 × 2 × 3 × 7 × 7 × 7

So here we may group them,

◕ 2 × 2

◕ 3

◕ 7 × 7 × 7

We may observe that only 7 has got repeated thrice and this is not the case with 2 & 3 and as we saw above for a number to be a perfect cube it has to have a number repeating thrice so to make 4116 a perfect cube,

➳ 2 × 3 × 3

➳ 2 × 3²

➳ 18

∴ 18 should be multiplied with 4116

Verification

»» 4116 × 18

»» 74088

Taking cube root

»» ³√74088

»» 74088 = 2³ × 3³ × 7³

»» 42

Hence Verified!!

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