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Question
Rationalise the denominator of the following:
`(sqrt(2) + 1)/(sqrt(2) - 1)`
Sum
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Solution
Given: `(sqrt(2) + 1)/(sqrt(2) - 1)`
Step-wise calculation:
Multiply the numerator and denominator by the conjugate of the denominator `sqrt(2) + 1`:
`(sqrt(2) + 1)/(sqrt(2) - 1) xx (sqrt(2) + 1)/(sqrt(2) + 1)`
= `(sqrt(2) + 1)^2/((sqrt(2))^2 - (1)^2`
Calculate numerator and denominator:
`(sqrt(2) + 1)^2`
= `(sqrt(2))^2 + 2 xx sqrt(2) xx 1 + 1^2`
= `2 + 2sqrt(2) + 1`
= `3 + 2sqrt(2)`
`(sqrt(2))^2 - (1)^2`
= 2 – 1
= 1
So, `(3 + 2sqrt(2))/1 = 3 + 2sqrt(2)`.
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