Question

Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`

`(1 + sqrt2)/(3 - 2sqrt2)`

Answer 1

We know that rationalization factor for `3 - 2sqrt2` is `3 + 2sqrt2`. We will multiply numerator and denominator of the given expression `(1 + sqrt2)/(3 - 2sqrt2)` by `3 + 2sqrt2` to get

`(1 + sqrt2)/(3 - 2sqrt2) xx (3 + 2sqrt2)/(3 + 2sqrt2) = (3 + 2 xx sqrt2 + 3 xx sqrt2 + 2 xx (sqrt2)^2)/((3)^2 - (2sqrt2)^2)`

`= (3 + 2sqrt2 + 3sqrt2 + 4)/(9 - 8)`

`= (7 + 5sqrt2)/1`

Putting te value of `sqrt2` we get

`7 + 5sqrt2 = 7 + 5(1.4142)`

= 7 + 7.071

= 14.071

Hence the given expression  is simplified to 14.071