Question

Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and  `sqrt5 = 2.236`

Answer 1

We know that rationalization factor for `sqrt5 - sqrt3` is `sqrt5 + sqrt3`. We will multiply denominator and numerator of the given expression `6/(sqrt5 - sqrt3)` by `sqrt5 + sqrt3` to get

`6/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) = (6sqrt5 + 6sqrt3)/((sqrt5)^2 - (sqrt3)^3)`

`= (6sqrt5 + 6sqrt3)/(5 - 3)`

`= (6sqrt5 + 6sqrt3)/2`

`= 3sqrt5 + 3sqrt3`

Putting the values of `sqrt5`  and `sqrt3` we get

`3sqrt5 + 3sqrt3 = 3(2.236) + 3(1.732)`

= 6.708 + 5.196

= 11.904

Hence value of the given expression is 11.904