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Question
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
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Solution
Let `E = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(3) + sqrt(2)`,
`E = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2)) xx (sqrt(3) + sqrt(2))/(sqrt(3) + sqrt(2))`
= `(sqrt(3) + sqrt(2))^2/((sqrt(3))^2 - (sqrt(2))^2` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `((sqrt(3))^2 + (sqrt(2))^2 + 2sqrt(3)sqrt(2))/(3 - 2)` ...[Using identity, (a + b)2 = a2 + b2 + 2ab]
= `3 + 2 + 2sqrt(6)`
= `5 + 2sqrt(6)`
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