Question

Express the following with rational denominator:

`1/(3 + sqrt2)`

Answer 1

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

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

`= (3 - sqrt2)/(9 - 2)`

`= (3 - sqrt2)/7`

Hence the given expression is simplified with rational denominator to `(3 - sqrt2)/7`