Question

Given that 2 is irrational, prove that (5 + 3 2) is an irrational number.​

Answer 1

Answer:

Step-by-step explanation:

Let us assume the contrary.

i.e; 5 + 3√2 is rational

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

3√2 = abab – 5

3√2 = a−5bba−5bb

Or √2 = a−5b3ba−5b3b

Because ‘a’ and ‘b’ are integers a−5b3ba−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.

Answer 2

Answer:

ur answer is in the ATTACHMENT