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Question
Prove that \[2 - 3\sqrt{5}\] is an irrational number.
Solution
Let us assume that \[2 - 3\sqrt{5}\] is rational .Then, there exist positive co primes a and b such that
`2-3sqrt5=a/b`
`3sqrt5=a/b-2`
`3sqrt5=(a/b-2)/3`
`sqrt5=(a-2b)/(3b)`
This contradicts the fact sqrt5 is an irrational number
Hence `2-3sqrt5` is irrational
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