Examine, Whether the Following Number Are Rational Or Irrational: `Sqrt5-2` - Mathematics

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Examine, whether the following number are rational or irrational:

`sqrt5-2`

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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.

  Is there an error in this question or solution?
Chapter 1: Number Systems - Exercise 1.4 [Page 31]

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RD Sharma Mathematics for Class 9
Chapter 1 Number Systems
Exercise 1.4 | Q 3.09 | Page 31

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