Prove that √(1+√3) is irrational, assuming that √3 is irrational
Given, is irrational.
To prove that is irrational.
Proof:
Assume is rational, so that , where a,b are co-primes and .
On left side, is irrational as it is given.
On right side, must be rational because is rational by assumption.
Now, an irrational cannot be equal to rational.
We get a contradiction.
So, our assumption is wrong.
Thus, is irrational.
Comments