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Question
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
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Solution
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5] xx [sqrt6 - sqrt5]/[sqrt6 - sqrt5]`
= `[(sqrt6 - sqrt5)^2]/[(sqrt6)^2 - (sqrt5)^2]`
= `[(sqrt6)^2 + (sqrt5)^2 - 2(sqrt6 xx sqrt5)]/[(sqrt6)^2 - (sqrt5)^2]`
= `[6 + 5 - 2sqrt30 ]/[(sqrt6)^2 - (sqrt5)^2]`
= `[11 - 2sqrt30 ]/[6 - 5]`
= `11 - 2sqrt30`
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