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Question
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
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Solution
The given number is `1/(sqrt5 + sqrt2)`
On rationalising the denominator,
⇒ `1/(sqrt5 + sqrt2) = 1/(sqrt5 + sqrt2) xx (sqrt5 - sqrt2)/(sqrt5 - sqrt2)`
We know that (a + b) (a - b) = a2 - b2
⇒ `1/(sqrt5 + sqrt2) = (sqrt5 - sqrt2)/((sqrt5)^2 - (sqrt2)^2)`
⇒ `1/(sqrt5 + sqrt2) = (sqrt5 - sqrt2)/(5 - 2)`
∴ `1/(sqrt5 + sqrt2) = (sqrt5 - sqrt2)/3`
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