Give an example of irrational numbers a and b such that the indicated expression is....?

Question

(a) irrational and (b)rational:

1. a+b

Answer 1

(a) (√2) / 2 is irrational. If you let a = (√2) / 2 and b = (√2) / 2, then their sum, √2, is also irrational.

(b) -√2 is irrational. √2 is also irrational. Their sum, (-√2) + √2, is 0, which is rational.

Answer 2

(a) irrational.
a = √2 + √3 is irrational.
Why?
Well, a² = 5 + 2√6, which is irrational
and if a were rational, a² would be also.

(b) rational.
π and 4-π are both irrational, but their sum is 4, which
is rational.