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Question
Examine, whether the following number are rational or irrational:
`(sqrt2-2)^2`
Solution
Let `x=(sqrt2-2)^2` be a rational number.
`x=(sqrt2-2)^2`
`rArrx=2+4-4sqrt2`
`rArrx=6-4sqrt2`
`rArr(x-6)/(-4)=sqrt2`
Since, x is rational number,
⇒ x – 6 is a rational nu8mber
`rArr(x-6)/(-4)` is a rational number
⇒ `sqrt2`is a rational number
But we know that `sqrt2` is an irrational number, which is a contradiction
So `(sqrt2-2)^2` is an irrational number
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