Question

Rationalize the denominator.

`3/(2 sqrt 5 - 3 sqrt 2)`

Answer 1

`3/(2 sqrt 5 - 3 sqrt 2)`

`= 3/(2 sqrt 5 - 3 sqrt 2) xx (2 sqrt 5 + 3 sqrt 2)/(2 sqrt 5 + 3 sqrt 2)` 

`= (3(2 sqrt 5 + 3 sqrt 2))/((2 sqrt 5)^2 - (3 sqrt 2)^2)`

.....`[("a" + "b")("a" - "b") = "a"^2 - "b"^2]`

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

`= (3(2 sqrt 5 + 3 sqrt 2))/(20 - 18)`

`= (3(2 sqrt 5 + 3 sqrt 2))/2`