It is quite easy to find the square root of a perfect square using the division method. Here are the steps with an example so that you can understand it. We will find the square root of 8464. To make life easy for you, here is the answer. The square of 8464 is 92. So here we go.
To start off, make a set of two digits. These sets are always made from right to left, which means the units and the tens place will make the first set and so on. You can put a horizontal line over the digits
to understand them even better. In this case, 64 will be the first set while 84 will be the second.But while solving the problem, 84 will be the first set to be considered. Now, consider all the smallest squares than 84. These are 1, 4, 9, 16, 25, 36, 49, 64 and 81. Now, when you divide, you have to pick the highest of them all – which is 81. This means, you have to start with the nearest square to the left most set.
The square root of 81 is 9. So, divide 84 by 9. The quotient is 9 and the remainder is 3. Add the quotient 9 to the divisor 9 to the left hand side. The sum here will be 18. Take the
next set, which is 64 and write it which should be preceded by the remainder – 3.The next dividend will be 364. Now, the taking the digits 1, 2, 3 … you have to determine, which digit has to be written next to the sum 18. In this case, the number is 2. Whichever digit you take on 18, you have to write the same digit next to the quotient. So, if you write 1 near 18, write 1 at the quotient’s place (this will make the quotient 91). If you write 2 next to 18, you have to write 2 next to 9 at the quotient’s place. Then multiply. Remember not to let this product go beyond 364.
The ideal digit here will be 2. So, write the ‘2’ next to 18, making it 182. Write the same ‘2’ next to 9 at the quotient. This will be 92 for now. Now, multiply 182 by 2. The product is 364. Subtract 364 from 364 to get 0 as the remainder.
Write the ‘2’ below 182 to add it. The final sum here would be 184. Always remember to check that the sum at the end of each step is twice the quotient. At the end of the first step, the quotient was 9 and the sum to the left was 18.
If you consider a number like 12,544 to find the square root, 44 will be the first set, 25 will be the second and the third set would consist of only one digit – which is 1 in this example.
