## 12. Given that √3 is irrational, prove that 5√3-2 is an irrational number .​

Question

12. Given that √3 is irrational, prove that
5√3-2 is an irrational number .​

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1 month 2021-08-17T06:23:22+00:00 2 Answers 0 views 0

1. Step-by-step explanation:

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.