12. Given that √3 is irrational, prove that 5√3-2 is an irrational number . Question 12. Given that √3 is irrational, prove that5√3-2 is an irrational number . in progress 0 Math Liliana 1 month 2021-08-17T06:23:22+00:00 2021-08-17T06:23:22+00:00 2 Answers 0 views 0

## Answers ( )

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.

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