Question

Light 823543 by the smallest number so that the quotient is a perfect cube .write the number and find the cube root of the quotient.

Answer 1

Answer:

Prime factorization of,

8748=(2×2)×(3×3×3)×(3×3×3)×(3)

In the first bracket there are two 2's and in the last bracket there is only one 3 and if these are removed then the number becomes perfect cube.

Hence smallest number which should be divided by 8748 so that the final number is a perfect cube=2×2×3=12

Hence required number=8748/12=729

Prime factorization of,

729=(3×3×3)×(3×3×3)

Therefore,cube root of 729=3×3=9

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