Question

Q.20) Is 3072 a perfect cube ? If not then by which smallest number should be multiplied so that the

quotient is a perfect cube?​

Answer 1

Answer:

hope this answer will help you

Answer 2

$Resolve \: 3072 \: into \: product \: of \: prime \: factors$

2 | 3072

________

2 | 1536

_________

2 | 768

_________

2 | 384

_________

2 | 192

_________

2 | 96

_________

2 | 48

_________

2 | 24

_________

2 | 12

_________

2 | 6

_________

*** 3

3072 = (2×2×2)×(2×2×2)×(2×2×2)×2×3

The prime factor 2 and 3 doesn't appear in a group of three.

So, 3072 is not a perfect cube.

Hence, the smallest number by which it is to be multiplied to make it a perfect cube is ( 2×2×3×3) = 36 .

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