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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.
`sqrt(2)/(2 + sqrt(2)`
Solution
Let `E = sqrt(2)/(2 + sqrt(2)`
For rationalising the denominator, multiplying numerator and denominator by `2 - sqrt(2)`, we get
= `sqrt(2)/(2 + sqrt(2)) xx (2 - sqrt(2))/(2 - sqrt(2))`
= `(sqrt(2)(2 - sqrt(2)))/((2)^2 - (sqrt(2))^2` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `(sqrt(2) xx sqrt(2)(sqrt(2) - 1))/2`
= `(2(sqrt(2) - 1))/2`
= `sqrt(2) - 1` ...[Put `sqrt(2)` = 1.414]
= 1.414 – 1
= 0.414
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