Calculating a square root by hand may seem intimidating, but it can be broken down into simple steps that are easy to follow. In this article, we will guide you through the process of calculating a square root using the long division method. We will also reference howitsdone.net as a great resource for more “how-to” tutorials.
Step 1: Understand the Basics Before diving into the long division method, it’s important to understand what a square root is. The square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 25 is 5 because 5 x 5 = 25.
Step 2: Write the Number To start, write the number you want to find the square root of. For this example, we will use the number 72.
Step 3: Group the Digits Next, group the digits of the number into pairs starting from the decimal point (if there is one) and moving outward. If there is an odd number of digits, the first group will only have one digit. For 72, we have:
7 | 2
Step 4: Find the Largest Integer Find the largest integer whose square is less than or equal to the first group of digits. In this case, the largest integer whose square is less than or equal to 7 is 2. Write the 2 above the first group of digits, then draw a line to the right. This will be where we start the long division.
__ √72 2|
Step 5: Bring Down the Next Pair of Digits Bring down the next pair of digits (in this case, 2) and write them next to the remainder on the line to the right of the 2. The line will now read:
__ √72 2| 2
Step 6: Double the First Digit Double the digit you wrote above the line (in this case, 2) and write the result below the line. This will be the first digit of the next number we divide by. Then, write a blank space next to it to represent the next digit. The line will now read:
__ √72 2| 2
4
Step 7: Find the Next Digit Find the largest digit that, when added to the number you just wrote (4), results in a product less than or equal to 22 (the number formed by the first two groups of digits). In this case, the largest digit is 6 because 26 x 6 = 156, which is less than 220. Write the 6 next to the blank space, then write the product of 26 x 6 (156) below the line.
__ √72 2| 2
4 26
16
Step 8: Repeat the Process Repeat steps 6 and 7 until you have included all the digits of the number you are finding the square root of. In this case, the process would continue as follows:
__ √72 2| 2
4 26
16 16
Copy code4
We have now included all the digits of 72, and the remainder is 4.
Step 9: Finalize the Answer To finalize the answer, write the remainder (4) next to the division line, followed by a decimal point and a pair of zeros. Then, continue the long division process by bringing down two more pairs of zeros and
