Actually there is no direct way to find out the square root of a number.
Most commonly used method is guess and multiply method
If I want to calculate the square root of 1764, I know the square root of 1600 in 40, and 1764 is very close it it. When i guess 43 as the square root, 43*43= 1849, It is too high.
Let us try 42 then, 42*42=1764, Oh!! we got it.
Most of the time you way need to do more number of iteration.
Another method id to factorize the number,This is the way I learned in lower grade school,
Let's take the same example,
First of all, Factorization is done as given in the picture below,
The number will be divided by smallest divisible again and again
Most commonly used method is guess and multiply method
If I want to calculate the square root of 1764, I know the square root of 1600 in 40, and 1764 is very close it it. When i guess 43 as the square root, 43*43= 1849, It is too high.
Let us try 42 then, 42*42=1764, Oh!! we got it.
Most of the time you way need to do more number of iteration.
Another method id to factorize the number,This is the way I learned in lower grade school,
Let's take the same example,
First of all, Factorization is done as given in the picture below,
The number will be divided by smallest divisible again and again
Now I can write 1764=2*2*3*3*7*7
Then, square root of 1764 is as same as the square root of (2*2*3*3*7*7), Now things are so simple.
As you know square root of 2*2 =2, In the same way, we can take one number out of each pair and multiply,
Then square root of 1764 = 2*3*7=42
If the number is not a square of a whole number, you will get a 2, 3, or 5 (prime number) without a pair,
For example square root of 20 is square root of (2*2*5), here 5 is alone, Then you can write only as square root of 20 is 2*(square root of 5)
So must know square root of some small prime numbers.