18 & 18. I like it.
The square root of a natural number won't be rational unless the number is a perfect square. So not a and not b but yes to C.
For d, -0.125374..., we can't really tell. The three dots tells us it goes on. There's no indication of a repeat but we can't assume it doesn't repeat either. For d the correct answer is cannot be determined.
OK, onto 18.
The square root of 12 is irrational so has a nonterminating, nonrepeating decimal expansion.
7/8 has a finite decimal expansion, 0.875. When the reduced denominator doesn't have any prime factors besides 2 and 5 we'll get a finite decimal expansion. Answer: b
5/11 has 11 as a factor in the denominator, so is an infinite repeating decimal.
I'll guess there's three dots after 0.81818181 so that one doesn't terminate either.
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Bonus
0.21 rational, equal to 21/100
3/12 rational, it's the ratio of integers
√12 - 2 is irrational because of the √12
4.125... can't really tell because the ... may hide a repeating or nonrepeating part.
