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प्रश्न
Prove that \[4 - 5\sqrt{2}\] is an irrational number.
उत्तर
Let us assume that \[4 - 5\sqrt{2}\] is rational .Then, there exist positive co primes a and b such that
`4-5sqrt2=a/b`
`5sqrt2=a/b-4`
`sqrt2=(a/b-4)/5`
`sqrt5=(a-4b)/5b`
This contradicts the fact that `sqrt2`is an irrational
Hence `4-5sqrt2` is irrational
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