Question

(how to do this sum ) prove prove that the following are irrational 7✓5​

Answer 1

Solution :-

Let us assume, to the contrary that 7√5 is rational.

Then, there exists co - primes a and b (b ≠0) such that

7√5 = a/b => √5 = a/7b

Since, a and b are integers, so a/7b is rational.

Thus, √5 is also rational.

But this contradicts the fact that √5 is irrational. So, our assumption is is incorrect.

Hence, 7√5 is irrational