Question

If √ab is an irrational number,prove that √a+√b is rational

Answer 1

Answer:

let ✓a + ✓b be rational no. p/q

then

✓a + ✓b = p/q

squaring on both the side...

(✓a + ✓b)² = (p/q)²

(✓a)² + (✓b)² + 2✓a✓b = p²/q²

we can write it as..

a + b + 2✓ab = p²/q²

.•. the no. also consist of ✓a✓b which is ✓ab

then it's also a irrational no. because

it's given that ✓ab is an irrational no.

H.P

Answer 2

Answer:

We have (√a+√b)^2= a+b+2√(ab)

From the question we see that the RHS is irrational

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