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Question
Examine, whether the following number are rational or irrational:
`sqrt5-2`
Solution
Let `x=sqrt5-2` be the rational number
Squaring on both sides, we get
`x=sqrt5-2`
`x^2=(sqrt5-2)^2`
`x^2=5+4-4sqrt5`
`x^2=9-4sqrt5`
`(x^2-9)/(-4)=sqrt5`
`rArr(x^2-9)/(-4)` is a rational number
`rArrsqrt5` is a rational number
But we know that `sqrt5` is an irrational number
So, we arrive at a contradiction
So `(sqrt5-2)` is an irrational number.
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