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Question
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Solution
`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`
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