Question

What is smallest number that should be divided by 10500 to make it perfect cube?

Answer 1

QUESTION :
What is smallest number that should be divided by 10500 to make it perfect cube?


To find the cube root by prime factorization :
Steps :
•Express the number as a product of prime factors.
•Make triplets of equal prime factors.
•Take one factor from each triplet and multiply them.


SOLUTION :
By Prime factorization ,
2 | 10500
-----------
2 | 5250
------------
5 | 2625
-----------
5 | 525
-----------
5 | 105
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3 | 21
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7 | 7
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1

10500 = (2×2)×(5×5×5)×(3) × (7)
Here, 2,3 & 7 do not form a triplet. Hence the Given number is not a perfect cube. We divide 10500 by (2×2×3×7) = 84 to make it a perfect cube.

10500/84 = (2×2)/(2×2) ×(5×5×5)×(3) /(3) × (7)/(7)
³√125 = (5×5×5) = 5
³√125 = 5

Hence, the smallest number that should be divided by 10500 to make it perfect cube is 84.

HOPE THIS WILL HELP YOU...