Question

Prove that √3+1 is irrational number?

Answer 1

the most basic without any mathematical prove is that if any integer is added to any irrational no. then the sum will be an irrational no. only

Answer 2

Let us assume that √3 + 1 is a rational number

Then , it is of the form p/q where p and q are integers and q =/= 0

So , √3 + 1 = p/q

=> √3 = p/q -1

=> √3 = (p - q)/q

Here (p-q)q is rational

So , √3 is also rational

But this contradicts the fact that √3 is irrational

This contradiction arises due to our wrong assumption that √3 + 1 is rational

Hence √3 + 1 is irrational

Hope it helped you...