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Question
Rationalise the denominator of the following:
`1/(sqrt7-2)`
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Solution
The given number is `1/(sqrt7 - 2)`
On rationalising the denominator,
⇒ `1/(sqrt7 - 2) = 1/(sqrt7 - 2) xx (sqrt7 + 2)/(sqrt7 + 2)`
We know that (a + b) (a − b) = a2 − b2
⇒ `1/(sqrt7 - 2) = (sqrt7 + 2)/((sqrt7)^2 - (2)^2)`
⇒ `1/(sqrt7 - 2) = (sqrt7 + 2)/(7 - 4)`
∴ `1/(sqrt7 - 2) = (sqrt7 + 2)/3`
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