Divide the number 8748 by the smallest number, so that the quotient is a perfect cube. Also find the cube root of the quotient.
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176
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
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
Answered by
5
Answer:
it is very easy answer 12 9
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