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))`

Answer 1

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