Question

The number 1953125 is equal to 5^9. explain how the information above informs you that 1953125 is not a square number

Answer 1

If 1953125 is a square number, then
`1953125=n^2,~n\in\mathbb{N}`

By what's given,
`1953125=5^9\Rightarrow n^2=5^9\Rightarrow n=5^(4.5)=625√(5)`

But
`n=625√(5) \\otin\mathbb{N}`, therefore, our assumption that 1953125 is a square number is wrong.