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Question
Rationalise the denominator of `(2 - sqrt(3))/(2 + sqrt(3))`.
Sum
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Solution
To rationalise the expression:
`(2 - sqrt(3))/(2 + sqrt(3))`
Step 1: Multiply numerator and denominator by the conjugate of the denominator `(2 - sqrt(3))`:
`(2 - sqrt(3))/(2 + sqrt(3)) xx (2 - sqrt(3))/(2 - sqrt(3)) = (2 - sqrt(3))^2/((2 + sqrt(3))(2 - sqrt(3))`
Step 2: Denominator
`(2 + sqrt(3))(2 - sqrt(3))`
= `2^2 - (sqrt(3))^2`
= 4 – 3
= 1
Step 3: Numerator
`(2 - sqrt(3))^2`
= `4 - 4sqrt(3) + 3`
= `7 - 4sqrt(3)`
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