There are certain facts you have to keep in mind to perform square root of number:-
Squares of numbers from 1 to 9 are 1, 4, 9, 16, 25, 36, 49, 64, 81.
Square of a number cannot end with 2, 3, 7, and 8. if it ends with them , then it is not perfect square root.
The square root of a number ending with 1 (1, 81) ends with either 1 or 9.
The square root of a number ending with 4 (4, 64) ends with either 2 or 8.
The square root of a number ending with 9 (9, 49) ends with either 3 or 7.
The square root of a number ending with 6 (16, 36) ends with either 4 or 6.
If the number is of ‘n’ digits then the square root will be ‘n/2’ OR ‘(n+1)/2’ digits.
Lets take 2704 (a perfect square) as an example to understand it better:-
The last digit of number is 4 so our expected square root should end with 2 or 8.
Find square of two numbers ending with 10, in between which given number lie. Taking 50 (2500)and 60(3600), 2704 lie in between them.
Now find to which square 2704 is closer to. Here it is closer to 2500. So the answer should be 52.
Hence square root of 1704 is 52
reference- Vedic Maths