Question

Prove that √p+ √q is an irrational number where p and q are primes.

Answer 1

Let √p + √q is rational number

A rational number can be written in the form of a/b

so

√p + √q = a/b

√p = a/b - √q

√p = ( a - b √ q ) /b

p, q are integers then ( a - b √q ) /b

it is a rational number

So √p is also rational number

So it contradicts that √p + √q is irrational number

So it is false that it is irrational number

it is a rational number √p