Question

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt2 - 1)/sqrt5`

Answer 1

We know that rationalization factor of the denominator is `sqrt5`. We will multiply numerator and denominator of the given expression `(sqrt2 - 1)/sqrt5`by `sqrt5` to get

`(sqrt2 - 1)/sqrt5 xx sqrt5/sqrt5 = (sqrt2 xx sqrt5 - sqrt5)/(sqrt5 xx sqrt5)`

`= (sqrt10 - sqrt5)/5`

Putting the value of `sqrt10`and `sqrt5` we get

`(sqrt10 - sqrt5)/5 = (3.162 - 2.236)/5`

`= 0.926/5`

= 0.1852

The value of expression 0.1852 can be round off tp three decimal places as 0.185.

given expression is simplified to 0.185