Question:If `sqrt (14)` = 3.7416, find the value of of `sqrt (2/7)` 

`sqrt (2/7)` 

=`sqrt ((2 xx 7)/(7 xx 7))`

=`sqrt ((14)/(7 xx 7))`

=`sqrt 14 /7`

=`3.7416/7`

=0.5345

Question:If `sqrt 15` = 3.8727, find the value of `((sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)))` 

=`((sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)))`

=`((sqrt(5) + sqrt(3)))/((sqrt(5) - sqrt(3))) x ((sqrt(5) + sqrt(3)))/((sqrt(5) + sqrt(3)))`

=`((sqrt(5) + sqrt(3))^2)/(5-3)`

=`(5 + 3 +2 sqrt(5) xx sqrt(3))/2`

=`(8 + 2sqrt(15))/2`

=`(4 + sqrt(15))`

=(4 + 3.8729)

=7.8729

Question:Evaluate: `sqrt ((.036 xx .025 xx .49)/(.81 xx .016 xx .064))` 

The sum decimal places in the numerator and the denominator of the redicand being the same, we may remove the decimal places
`:.` Given Expression = `sqrt ((36 xx 25 xx 49)/(81 xx 16 xx 64))`

=`((6 xx 5 xx 7)/(9 xx 4 xx 8))`

=`35/48`

Question:Find the cube root of 2744. 

Resolving 2744 as the product of prime factors, we get:
2744 = `2^3` x `7^3`. 
`:.` `2744^((1/3))` = (2 x 7)
=14

Question:Find the average of all prime numbers between `30` and `50`. 

There are five prime numbers between `30` and `50`.
Thet are `31,37,43` and `47.`

`:.` Require average = `(31 + 37 + 43 + 47)/5`

`=199/5`

`=39.5`

Question:Find the average of first 30 natural numbers. 

Sum of first 30 natural numbers =`((30 xx 31)/2)` = 465
`:.` Required average = `465/30` = 15.5

Question:Find the average of first 25 multiples of 3. 

Required average = `(3(1 + 2  + 3 + ..... +25))/25`
=`((3 xx 25 xx 26)/(2 xx 25))`
=39

Question:The average age of a class of `39` students is `15` years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher. 

Total age of 39 persons 

`= (39 x 15)` years 

`= 585` years.

 Average age of 40 person 

`= 15` years `3` months 

`= 61/4` years.

 Total age of the 40 person 

 `= (61/4) xx 4` 

 years `= 610` years.

`:.`Total age of 40 person 

 `= (610 - 585)` 

 Years `= 25` years.

Question:The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher? 

The total age of 39 persons =(39 x 15) years = 585 years.
Average age of 40 person =15 years 3 months =`(61/4)` years.
Total age of 40 person = `(61/4 xx 40)` years =610 years.
`:.` Age of the teacher= (610 x 585) years = 25 years.

Question:The average weight of `10` oarsmen in a boat is increased by `1.8 kg` when one of the crew, who weights `53` kg is replaced by a new man. Find the weight of the crew, who weights `53 kg` is replaced by a new man. Find the weight of the new man. 

Total weight increased 
`= (1.8 xx 10)` kg 
`=18` kg.

`:.` Weight of the new man 
`= (53 + 18 )` kg 
`=71` kg