Question

Rationales the denominator and simplify:

`(1 + sqrt2)/(3 - 2sqrt2)`

Answer 1

We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2`

`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2sqrt2 + 3sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`

` = (3 + 5sqrt2 + 4)/(9 - 4 xx 2)`

`= (7 + 5sqrt2)/(9 - 8)`

`= (7 + 5sqrt2)/1`

`= 7 + 5sqrt2`

Hence the given expression is simplified to `7 + 5sqrt2`