Question

How do you rationalize the denominator and simplify `3/(2-sqrt2)`?

Answer 1

`(6 + 3sqrt(2))/2`

Explanation:

Rationalize the denominator with the factor `(2+sqrt(2))`

Hence: `3/(2-sqrt(2))` = `3((2 + sqrt(2)))/((2-sqrt2)(2+sqrt(2))`

=`3((2+sqrt(2)))/(4+2sqrt(2)-2sqrt(2)-2)`

= `(6 + 3sqrt(2))/2`