Question

1. Prove by the method of contradication
that ^5 is irrational​

Answer 1

Let ^5 be rational

Therefore ^5=a/b ( let a and b be co-prime)

=>5 =a2/b2

=>5b2=a2

Since, a2 is divisible by 5

Therefore, a is divisible by 5

Let, a =5c

=> a2 =25 c2

=>5b2=25 c2 (Since, a2= 5 b2)

=> b2 = 5c2

Therefore, b2 is divisible by 5

Therefore, b is divisible by 5

But this contradicts the fact that a and b are co-prime.

This contradiction has arisen because of our incorrect assumption that ^5 is rational.

So, we conclude that ^5 is irrational.

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