Question

PLEASE ANSWER 18 AND 18

Answer 1

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.

---------

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.