Prove that √p + √q is irrational, where p and q are primes
Let us suppose that √p + √q is rational.
Let √p + √q = a where a is rational number.
⇒ √p = a – √q
On squaring both side we get
[Using formula ]
The above statement is a contradiction as the right hand side is a rational number, where the left hand side i.e. √q
is irrational, since p and q are prime numbers.
So, our assumption is wrong.
Hence, √p + √q is rational.