Question

Giving reason in each case, show that each of the following numbers is irrational.
1. 5√7
​

Answer 1

Answer:

Let us assume that 5+7 is a rational number.

Then 5+7=qp, where p and q are two integers and q=0

⇒7=qp−5=qp−5q

Since, p, q and 5 are integers, so qp−5q is a rational number.

Therefore 7 is also a rational number.

But this contradicts the fact that 7 is an irrational number.

This contradiction has arisen due to our assumption that 5+7 is a rational number.

Hence, 5+7 is an irrational number.