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.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.