Question

Question :- if r is rational and s is irrational, then r + s and r - s are irrational numbers, and rs and r/s are irrational numbers, r ≠ 0.



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Answer 1

Answer:

Irrational

1 is rational

2–√ is irrational

We cannot have 1+2–√=pq , where p∈Z and q∈N

Answer 2

Answer:

good morning I think the answer is

Step-by-step explanation:

You can easily prove that adding two rational numbers gives you another rational number. If R is a rational number, so is -R. So, that also is true for subtraction. The formal way to say this is that the rational numbers are closed under addition and subtraction.

If R+S and R are rational numbers, then (R+S) - R also will have to be a rational number, which means that S would have to be a rational number. Since S is not a rational number, then the initial premise that “R+S and R are rational numbers” is not true. So, if R is a rational number, then R+S cannot be a rational number when S is an irrational number. (Note that if R is not a rational number, then R+S can be rational or irrational.)

hope this will help you