Hello All,

I had a few finite examples from my text I had some questions about. They are discussing Q[Sqrt(-5)] , and I know that it is i*Sqrt(5) = Sqrt(-5). Given this information, it gives some examples and it said I should be able to identify which examples are in Q[Sqrt(-5)]

Example 1: 2+3*Sqrt(-5)

Example 2: (3+8*Sqrt(-5))/2

Example 3: (3+8*Sqrt(-5))/5

Example 4: 3/5

Example 5: i*Sqrt(-5)

From observation I inferred that Example 5 was in Q[Sqrt(-5)], but then i noticed that it says i*Sqrt(-5) and not i*Sqrt(5). I don't understand how Example 4 could be part of a negative rooted Quadratic field either.

Could someone explain these? If you could, please provide a small reason as to why each one is or isn't part of Q[Sqrt(-5)].

Thank you, all the help is appreciated!