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`

`3/sqrt10`

Answer 1

 We know that rationalization factor of the denominator is `sqrt10`. We will multiply numberator and denominator of the given expression `3/sqrt10` by `sqrt10to get

`3/sqrt10 xx sqrt10/sqrt10 = (3 xx sqrt10)/(sqrt10 xx sqrt10)`

`= (3sqrt10)/10`

`= (3 xx 3.162)/10`

`= 9.486/10`

= 0.9486

The value of expression 0.9486 can be round off to three decimal places as 0.949.

Hence the given expression is simplified to 0.949.