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Question
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
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Solution
The given number is `1/(sqrt7 - sqrt6)`
On rationalising the denominator,
⇒ `1/(sqrt7 - sqrt6) = 1/(sqrt7 - sqrt6) xx (sqrt7 + sqrt6)/(sqrt7 + sqrt6)`
We know that (a + b) (a + b) = a2 - b2
⇒ `1/(sqrt7 - sqrt6) = (sqrt7 + sqrt6)/((sqrt7)^2 - (sqrt6)^2)`
⇒ `1/(sqrt7 - sqrt6) = (sqrt7 + sqrt6)/(7 - 6)`
∴ `1/(sqrt7 - sqrt6) = sqrt7 + sqrt6`
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