1. 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.

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,