Question

27. Prove that 5 + 3/2is an irrational number.​

Answer 1

Answer:

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:

Let us assume the contrary.

i.e; 5 + 3√2 is rational

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

3√2 = a /b – 5

3√2 =  a−5b /b

Or √2 =  a−5b /3b

Because ‘a’ and ‘b’ are integers a−5b/3b is rational.

So, 5 + 3√2 is irrational.

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