- Find the smallest number by which 8640 must be divided so that the quotient is a perfect cube. Also find the cube root of the number so obtained.

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Find the smallest number by which 8640 must be divided so that the quotient is a perfect cube. Also find the cube root of the number so obtained.

Solution:

8640=**2 ×2 ×2** ×**2 ×2×2**×**3×3×3**×5

Now, forming the triplets , only 5 is extra factor.

therefore, dividing 8640 by 5 ,we get,1728

perfect cube = 1728 = 2**×**2**×**2**×**2**×**2**×**2**×**3**×**3**×**3

hence,

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