Question

Check whether the square of the following is rational or irrational:

`3 + sqrt(2)`

Answer 1

`(3 + sqrt(2))^2`
= `(3)^2 + (sqrt(2))^2 + 2 xx 3 xx sqrt(2)`
= 9 + 2 + 6`sqrt(2)`
= 11 + 6`sqrt(2)`, which is irrational