Question

please tell all the answer by hcf

Answer 1

Hi, my friend here is your answer

(1) 216
Its prime factorization is 2×2×2×3×3×3
Here we get
3√216= 2×3 = 6
It is a perfect cube.


(2) 128
its prime factorization is 2×2×2×2×2×2×2
Here number of 2s is 7and we know that 7is not divisible by 3. So, 128is not a perfect cube.

(3) 1000
Its prime factorization is 2×2×2×5×5×5
Here 2s and 5s are three here so, it is a perfect cube.


(4) 100
Its prime factorization is2×2×5×5
Here 2s and5s are 2each and not divisible by 3
It is not a perfect cube.

(5) 46656
Its prime factorization is 2×2×2×2×2×2×3×3×3×3×3×3
So, here 2s and 3s are 6 and 6is divisible by 3.
It is a perfect cube.


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