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प्रश्न
Show that \[5 - 2\sqrt{3}\] is an irrational number.
संख्यात्मक
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उत्तर
Let us assume that `5-2sqrt3` is rational .Then, there exist positive co primes a and b such that
\[5 - 2\sqrt{3}\] `=a/b`
`2sqrt3=a/b-5`
`sqrt3=((a/b)-5)/2`
`sqrt3= (a-5b)/(2b)`
This contradicts the fact that `sqrt3` is an irrational
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