Question

If a is rational and b is irrational, is a + b necessarily irrational? What if a and b both are irrational?

Answer 1

Lets see who can answer this one.

Answer 2

1) b is irrational => b =p/q for some integers. a not = d/c for any integers. a + b = a + p/q = X.
if X - rational, then b + X is rational too. So a+b irrational.

Answer 3

2) Pi is irrational and - Pi is irrational too, so a+b may be rational.

Answer 4

note that ur using wrong defintion, a number is a rational if it can be written as p/q where q is not equal to 0 and p and q are in their lowest terms

Answer 5

the way u have proved it is absurd and not understandable at all

Answer 6

Hint: prove part 1 by contradiction

Answer 7

I see. Let's a is irrational, b is rational an X = a + b. If X is rational then X-b is rational too,
but X-b=a contradiction

Answer 8

i cant say if thats the right way for proving with contradiction

Answer 9

Since a is rational, then a can be written as p/q,q not equal to 0
a+b=p/q+b=X
p/q=b-X
b-X can't be rational if X is rational since p/q is rational
X has to be irrational
i think i like nakita's form

Answer 10

look at this, assume a + b is rational, then b = (a+b) - a which is rational since a is rational. But, b is irrational. A Contradiction. Hence the assumption is wrong. Therefore, a + b is irrational

Answer 11

ok that is pretty lol

Answer 12

very nice. I should learn this.

Answer 13

nobody yet proved part 2