Square roots of non-perfect square , Mathematics Tricks and Fun 23

 Square roots of non-perfect square , Mathematics

 Tricks and Fun 23

Hello friends,today we are going to study how to derive

 the square roots of nonperfect squares. This is the 23rd class of Mathematics Tricks and Fun. I am Dr Prema B Sejekan. 

In this example we have to derive the square of 52443907.This is an eight digit number. So in the answer we will have 4 digits and rest will be in decimals.Since even number take first two digits ie 52.Find a digit the square of which is near to 52 ie 7.Now put seven on quotient side and 49 placed below 52 balance 3 in front

 of 4. Double of 7 ie 14 is taken as the divisor place it on the outer side and diary dividing 34 with 14 we will put 2 on quotient side and 28placed below 34 balance 6 we

 will put in front of 4 to form 64.Now square of 2 is 4 , 

deduct 4 from 64 ,we will get 60 which when divided by

 14 gives 4 as quotient.4×14=56.balance of 56 from 60

 is 4 placed beside 3 to give 43 .Now double of the 

product of 2 and 4(quotient) is 16 .deduct this from 43 gives 27.on dividing this by 14 gives 1 as quotient and 

13 balance is placed in front of 9 to give 139 . Double of product of 2 and 1 added to square of ,4 gives 20 deduct this from 139 gives 119 .On dividing this by 14 gives 8 as quotient and balance of 112 from 119 gives 7 placed in front of 0.subtract double the product of 2 and 8 added with double the product of 4 and 1 gives 40 balance of

 this from 70 is 30 .Divide this 30 by 14 gives 2 as 

quotient and remainder is 2.we can stop here since the question is up to 2 decimal places.So the answer is 7241.82

 In this we have to find the square root up to 4 decimal places. Since the question has 4 digits ,square root will have 2 digits rest will be in decimals which we will 

derive adding zero to remainder.Since even number we 

will take 13 first 3×3 is 9 place 3 on quotient side.

Subtract 9 from 13 gives 4 So next dividend is 48.Now double of 3 is 6 which dividing 48 gives 7 as quotient .subtracting ,42

 from 48 gives 6placed infront of 7 Now subract square

 of 7 ie 49 from 67 gives 18.dividing this by 6 gives 2 as quotient and subtracting 12 from 18 gives 6 add zero to this gives 60 from which double of the product of 7 

and 2 is deducted gives 32 as new dividend. On dividing with 6 gives 4 .6×4=24 . 24 deducted from 32 gives 8 

add zero to 8 gives 80 continue dividing as said till you

 get 4 decimals.The answer is 37.2424

 Here we have to find the square root of •000924016.put decimal point then one zero and take 09 as dividend 3×3

 is 9 so put 3 as quotient next to zero and continue dividing as said till 5 decimals.

Here square root of 20736.since odd number take two as first dividend 1as quotient balance 1 placed on front of 0 .double of 1 is two taken as divisor.10÷2 take 4×2 =8 Balance 2 infront of 7 deduct square of 4 from this gives 11 divide this by 2 gives again 4 as quotient and 3 as balance deduct double the product of 4 and 4 gives 1 as balance place zero on quotient side and take 1 to place infront of of 6 to give 16 .last digit on quotient side is 4 square of which deducted from 16 gives zero so this is a perfect square.

 Thank you in the coming class we will study cube roots .subscribe to my channel