The smallest postive natural number n for which 125×n is a perfect square number​

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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

Showing that 5^4 = 625 is a perfect square number.

So because p = 1, this makes n = 5^p = 5^1 = 5.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

answer: c i think

step-by-step explanation: