Question

Show that 10+5√2 is irrational

Answer 1

Let us assume the contrary.

i.e; 5 + 3√2 is rational

∴ 5 + 3√2 = ab, where ‘a’ and ‘b’ are coprime integers and b ≠ 0

3√2 = ab – 5

3√2 = a−5bb

Or √2 = a−5b3b

Because ‘a’ and ‘b’ are integers a−5b3b is rational

That contradicts the fact that √2 is irrational.

The contradiction is because of the incorrect assumption that (5 + 3√2) is rational.

So, 5 + 3√2 is irrational.