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)`

Answer 1

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