Question

√a+√b and a-b are rational numbers. Prove that √a, √b, a and b all are rational.
plz answer it step by step with full explanation.​

Answer 1

Answer:

That gives √a+√b=(1+q)√a, hence √a is rational and a is the square of a rational number, so the same holds for b. Now all you have to do is multiply √ab and √a+√b. Then we get b√a+a√b is rational. If a=b there is nothing to prove .