Question

Prove that √a+ √bis an irrational number. If √ab is irrational

Answer 1

Step-by-step explanation:

We have

$(\sqrt{a } + \sqrt{b} ) {}^{2} = a + b + 2 \sqrt{ab}$

From the question we see that the RHS is irrational

But if √a+√b were rational, the LHS would be rational.