Examine, whether the following numbers are rational or irrational: `(sqrt(2)+2)^2` (ii) `(5+sqrt(5))(5-sqrt(5))` `6/(2sqrt(3))`

Explanation

`(i) (sqrt(2)+2)^2`
`(sqrt(2)+2)^2`=x(rational)
`2+4+4sqrt2=x`
`(x-6)/4=sqrt2`
So, `(sqrt2+2)^2` is on irrational
`(ii) (5+sqrt(5))(5-sqrt(5))`[Rational]
`5^2-(sqrt5)^2`
`25-5`
`20`
`(ii)6/(2sqrt3)`
`3/(sqrt3)`
`sqrt3`[ is on irrational number]