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Question
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Solution
`1/(3 sqrt 5 + 2 sqrt 2)`
`= 1/((3 sqrt 5 + 2 sqrt 2)) xx ((3 sqrt 5 - 2 sqrt 2))/((3 sqrt 5 - 2 sqrt 2))`
` = ((3 sqrt 5 - 2 sqrt 2))/((3sqrt5)^2 - (2sqrt 2)^2)
...[(a+b)(a-b) = a^2 - b^2]`
`= ((3 sqrt5 - 2 sqrt 2))/(45-8)`
`= (3 sqrt5 - 2 sqrt 2)/37`
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