Question

Examine, whether the following number are rational or irrational:

`sqrt5-2`

Answer 1

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.