Calculate the square root of 625.
Step 1: Divide the number into pairs of digits,
starting from the right. If there is an odd number of digits, the
leftmost digit will be by itself.
6
25
Step 2: Find the largest digit that will go into the
leftmost group of digits that many times, and put that as the
quotient.
In this case, 2 will go into 6 two times. Two is the largest digit,
because 3 will not go into 6 three times.
Step 3: Multiply the divisor by the largest digit,
and subtract the product from the leftmost group of digits.
In this case, multiply 2 by 2, and subtract 4 from 6 for a remainder
of 2.
Step 4: Bring down the next group of digits to form
the new dividend, and double the quotient to form the new divisor.
In this case, bring down 25 to form 225 as the new dividend, and
double 2 to form 4 as the new divisor.
Repeat step 2: Find the largest digit that can be
appended to the new divisor such that the resulting number will go
into the new dividend that many times, and append that to the
quotient.
In this case, 45 will go into 225 five times. Five is the largest
digit, because 46 will not go into 225 six times.
Repeat step 3: Multiply the divisor by the largest
digit, and subtract the product from the dividend.
In this case, multiply 45 by 5, and subtract 225 from 225 for a
remainder of 0.
Repeat step 4: If there are no more digits, the
process is complete, and the quotient is the square root of the
number. In this case, the quotient is 25, so the square root of 625
is 25. If there are more digits, complete step 4, and repeat steps
2-4.