Question

find the smallest number by which 81920 must be divided to obtaun a perfect cube​

Answer 1

81920 = 2×2×2×2×2×2×2×2×2×2×2×2×2×2×5

We observe that the prime factor 5 does not form a pair.

Therefore, we must divide the number 5 so that the quotient becomes perfect square.

81920÷5 = 16984

16984 = 2×2×2×2×2×2×2×2×2×2×2×2×2×2

Now, each prime factor occurs in pairs. Therefore the required smallest number is 5

16984 = 2×2×2×2×2×2×2 = 128