Question

Give examples for sum of two irrationals to be (a) irrational (b) not an irrational​

Answer 1

Answer:

(a). let one number be √5 and other be -√5

then their sum will be = √5 + (-√5) = 0 ; rational

(b). let one number be 2√5 and other be 5√5 then their sum be = 2√5 + 5√5 = 7√5 ; irrational

Answer 2

Answer:

(a) $\sqrt{5} + \sqrt{2}$ is irrational as It can not be written in the form of p/q where p and q are integer and q$\neq$0

(b) $(3+\sqrt{2}) + (- \sqrt{2} ) = 3$ is rational as 3 can be written in the form of p/q where p = 3 and q=1.