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Question
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Solution
Let `E = (2 + sqrt(3))/(2 - sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `2 + sqrt(3)`,
`E = (2 + sqrt(3))/(2 - sqrt(3)) xx (2 + sqrt(3))/(2 + sqrt(3))`
= `(2 + sqrt(3))^2/((2)^2 - (sqrt(3)^2)`
= `(2^2 + (sqrt(3))^2 + 2 xx 2 xx sqrt(3))/(4 - 3)` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `4 + 3 + 4sqrt(3)` ...[Using identity (a + b)2 = a2 + 2b + b2]
= `7 + 4sqrt(3)`
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