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Question
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`1/(sqrt(3) + sqrt(2))`
Solution
Let `E = 1/(sqrt(3) + sqrt(2))`
For rationalising the denominator multiplying numerator and denominator by `sqrt(3) - sqrt(2)`, we get
= `1/(sqrt(3) + sqrt(2)) xx (sqrt(3) - sqrt(2))/(sqrt(3) - sqrt(2))`
= `(sqrt(3) - sqrt(2))/((sqrt(3))^2 - (sqrt(2)^2)`
= `(sqrt(3) - sqrt(2))/(3 - 2)`
= `sqrt(3) - sqrt(2)` ...`["Put" sqrt(3) = 1.732 "and" sqrt(2) = 1.414]`
= 1.732 – 1.414
= 0.318
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