Examine, Whether the Following Number Are Rational Or Irrational: `(Sqrt2-2)^2` - Mathematics

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Examine, whether the following number are rational or irrational:


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Let `x=(sqrt2-2)^2` be a rational number.





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

Concept: Concept of Irrational Numbers
  Is there an error in this question or solution?


RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.4 | Q 3.06 | Page 31

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