Numbers

# Can you add an irrational number and a rational number?

###### Wiki User

###### November 15, 2008 5:20AM

Let `a` be a rational number and `b` be an irrational number,assume that the sum is rational.

1.a +b =c

Where a and c are rational and b is irrational.

2.b=c-a

Subtracting the same number a from each side.

3.b is irrational c-a is a rational number we arrived at a contradiction.

So the sum is an irrational number.

## Related Questions

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### Explain why the sum of a rational number and an irrational number is an irrational number?

Let R1 = rational number
Let X = irrational number
Assume R1 + X = (some rational number) We add -R1 to both sides,
and we get: -R1 + x = (some irrational number) + (-R1), thus X =
(SIR) + (-R1), which implies that X, an irrational number, is the
sum of two rational numbers, which is a contradiction. Thus, the
sum of a rational number and an irrational number is always
irrational. (Proof by contradiction)