Question

By which least number 250*512 should be divided to make it a perfect square

Answer 1

Step-by-step explanation:

{The given number is,}The given number is, 

{250}250 × {512}512 

{Lets resolve 250 in prime factors}Lets resolve 250 in prime factors ,

250 = 2×5×5×5

=> 250 = (2) × (5)^3

So 250 is not a perfect cube.

{Lets resolve 512 in prime factors}Lets resolve 512 in prime factors ,

512 = 2×2×2×2×2×2×2×2×2

=> 512 = (2)^3 × (2)^3 × (2)^3

So 512 is a perfect cube.

Lets comeback to the question ,

{250}250 X {512}512 = (2) × (5)^3 × (2)^3 × (2)^3 × (2)^3

We can clearly see that, 

If digit 2 is divided from the term,then it will be a perfect cube all together.

The least number by which {250}250 ×{512}512 should be divided to make it perfect cube is 3 .

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