Find the value of three places of decimals; of each of the following. It is given that `sqrt(2)=1. 414 ,\ sqrt(3)=1. 732 ,\ sqrt(10)=3. 162` and `sqrt(5)=2. 236` (approx). (i) `(sqrt(2)+1)/(sqrt(5))` (ii) `(2-sqrt(3))/(sqrt(3))` (iii) `(sqrt(10)-\ sqrt(5))/(sqrt(2))`

Explanation

(i) Given :
`(sqrt2+1)/(sqrt(5))`
Multiplying the numerator and denominator of the given number by `sqrt5`
i.e,
`(sqrt2+1)/(sqrt(5))=(sqrt2+1)/(sqrt(5))xxsqrt5/sqrt5`
`=((sqrt2+1)sqrt5)/5=((1.414+1)xx2.236)/5=1.079`
(ii) Given :
`(2-sqrt3)/(sqrt(3))`
Multiplying the numerator and denominator of the given number by `sqrt3`
i.e,
`(2-sqrt3)/(sqrt(3))=(2-sqrt3)/(sqrt(3))xxsqrt3/sqrt3`
`=((2-sqrt3)sqrt3)/3=((2-1.732)xx1.732)/3=0.154`
(iii) Given :
`(sqrt10-sqrt5)/(sqrt(2))`
Multiplying the numerator and denominator of the given number by `sqrt2`
i.e,
`(sqrt10-sqrt5)/(sqrt(2))=(sqrt10-sqrt5)/(sqrt(2))xxsqrt2/sqrt2`
`=((sqrt10-sqrt5)sqrt2)/2=((3.162-2.236)xx1.414)/2=0.654`