square root tricks by Vedic maths

square root tricks by vedic maths

Hello friends in this 22 nd class on mathematics tricks and fun today we will learn how to find the square root 

by Vedic Maths I am Dr Prema b sejekan.. Armed with straight division and Urdhwa Tiryak sutra we will quickly solve the problems easily.

This is just a reminder how to do squaring using Urdhwa Tiryak sutra.when two digits square of the first digit then multiply the given two digits and double the product , 

when 3 digits twice the product of the first and third 

digit added to the square of the middle digit,when four digits twice the product of the first and last digits added to 

twice the product of the middle two digits.

Now coming to the principles of finding the square root,

First arrange into gps of two,

If there is one extra single digit that will be counted as a separate gp,

The number of digits in the square root will be same as the number of groups thus made.

In the case of pure decimals the number of digits in the square will be doubled than that in the square root 

you should know the square of 9 natural numbers at

 least

 square of 1 is 1, 2 square is 4,3 square is 9, 4 square is

 16, 5 square is 25 , 6 square is 36 , seven square is 49, 8 square is 64, 9 square is 81 10 square is 100, I will tell additional 10 digits square also hear 11 square is 121,12 square is 144 13 square is 169, 14 square is 196, 15 square 225 , 16 square is 256, 17 square is 289, 18 

square is 324, 19 square is 361 , 20 square is 400. We should note 3 points which will help us to solve the

 square root easily .Now digits which are compliments from 10 share the same last digits. one square and 9 Square One, 2 square and 8 square 4 as last digit,

 3 square and seven square 9 is the last digit , 4 square and 6 square 6 is the last digit , 5 square has 5 as the

 last digit 

Second point to note is digits 2 ,3,7 and 8 doesn't come 

as the last digit in all these squares

1,5,6,& 0 has the same last digit

We will do the square root of 3 to 4 digits example 121 first group into two groups 1 and 21 two groups are available. Now the last digit is 1 so it will fall into one square or nine square and the first digit is one so you should think you should choose the last digit 1 or 9 now we can add this number to the first digit so one+one

 gets two which is the middle digit in the answer . so the answer is √121=11.

√144,1,44,first digit is 1 second digit is 4 so it can be either 2 or 8 square. Twice the product of 1 and 2 is 4 So the square root of 144 is 12 

Now the square root of 169 grouping 1 and 69 first digit 

is one last digit is 9 it can be a square of 3 or square of seven . Now square of 3 is 9 and twice the product of 1 and 3 is 6 . so the square root of 169 is 13 .Now square root of •0064 is •08

square root of point 0 9 •3

 square root of point 9 that means square root of point

 90 the answer is •9.

 We Will take two examples here how to find square root using Straight division first example square root of 529 three digits so two groups 5 and 29 . We will take first 5. we have to find the digit the square of which will be near

 to 5. So 2×2 is four ,5 - 4 and balance one . We will put one in front of two to get 12. now as the divisor is the double the first quotient so double of 2 is 4 . so 4 is the divisor here . now 12 / 4 is 3 so balance is zero now we have the second quotient is 3 and using the square of 3 ,we can divide the second digit 9 - 9 balance is zero .So the answer is square root of 529 is 23 .

Next we have square root of

 11 9716 so there are 6 digits here that means three groups the answer will have 3 digits in the answer now first will take in 11 will find a digit double of which will 

go into 11 so 3 × 3 is 9, 11 we can divide by 3, 9 and balance of 2 which we will place beside 9 to give 29

 now double of 3 is 6 . 6 is the divisor , divide 29 using 6. 6×4 is 24 so will write four on the quotient side and 24

 we will place right below 29 and the balance 5 will put

 in front of 7 to give 57. now square of 4 is 16 will write

 16 below 57 and the balance is 41 now we have to

 divide 41 using 6 . 6 ,×6 is 36 so will write 36 below 41, balance will come 5 will write in front of 1 to give 51 

. now we have to cross multiply 4 and 6 that means

 4 x 6 and twice the product we can take ie 24 × 2 is 48

 will deduct 48 from 51 balance will be 3 will put 3

 besides 6. We get 36 now the square of the last digit 6

 is 36 , will substract 36 from the top 36 so the balance

 is zero. There is no reminder and this is a complete or a perfect square . the square root of 119716 is 346.

Here we have to find the square root of 6 digit number 55 2049 so the square root should have 3 digits now first we will take 55 we have to find the digit the square which will be near to 55. so 7 × 7 is 49 and balance is 6 . We will write 7 on the quotient side and 49 below 55 and 

balance 6 will put in front of two to give 62 next double

 of 7 that

 is 14 is taken as the divisor. now 62 should be divided 

by 14 . 4 × 14 is is 56 we will subtract 56 from 62 will

 get balance 6 which we'll put in front of 0 to give 60

. Now square of 4 is 16 will subtract 16 from 60 to give balance 44. This 44 is divided by 14 quotient 3 will go 

to give 42 with a balance of two which we will put in 

front

 of 49 to give 249 . This 249 can be divided by twice the product of 4 and 3 ie 24 . will subtract 24 next

 remaining is 9 . The square of 3 is 9 so there is no balance so this is a perfect square.√552049 is 743 

In the coming class we will learn more examples on square root. Thank you.subscribe to my channel.