Answer: 5
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Explanation:
125 = 5^3
If n = 5^p, where p is some positive whole number, then
125n = 5^3*5^p = 5^(3+p)
So that's why I made n some power of 5.
To be a perfect square, the exponent 3+p must be even
Since we want 125n to be as small as possible, we'll go with the smallest possible p here which is p = 1. Note how 3+p = 3+1 = 4 is even.
Furthermore, note that 5^(3+p) = 5^4 = 625
The square root of 625 is 25
We could write it like this
[tex]\sqrt{5^4} = \sqrt{(5^2)^2} = 5^2 = 25[/tex]
Showing that 5^4 = 625 is a perfect square number.
So because p = 1, this makes n = 5^p = 5^1 = 5.
