In that case we repeat steps 4, 5 and 6 until we reach any accuracy we want. In reality, numbers consist of many digits, including the ones after the decimal point. This way I could show the rules for solving square root problems. Note: I chose a perfect square (2025 = 45 x 45) on purpose. The result is zero, which means the task is complete. Subtract the product we calculated (which is 425) from the current number on the left (also 425). Write 5 next to 4 in the top right corner. 85 times 5 results in 425, which is exactly what we need. The number 8 and the number 5 give us 85. The result 516 is greater than 425, so we go lower and try 5. It must be the largest possible integer that allows the product to be less than or equal the number on the left.įor example, if we choose the number 6, the first number becomes 86 (8 and 6) and we must also multiply it by 6. Time to fill in each blank space with the same integer (i). This results in 8 and we write it in the bottom right corner followed by _ x _ = Now multiply the number in the top right corner (which is also 4) by 2. We write it next to the subtracted value already there (which is 4). Next, let's move down the next pair in our number (which is 25). The result equals 4 and we will write it as shown above. Now we need to subtract the square of that integer (which equals 16) from the leftmost number (which equals 20). Let’s deposit 4 to the top-right corner and 4² = 16 to the bottom right one. Since 4² = 16 20, the integer in question is 4. In our current example the leftmost number is 20. STEP 2: Find The Largest IntegerĪs the next step, we need to find the largest integer (i) whose square is less than or equal to the leftmost number. Or in the case of a number with an odd amount of digits such as 19,036, we will start with 1 90 36. Then, let’s separate the number’s digits into pairs moving from right to left.įor example, the number 7,469.17 becomes 74 69. We will divide the space into three parts. To make this article more reader friendly, each step comes with illustrations. The one I want to share with you is one of them. Yes we can, and there are several different methods. What if there is no calculator or a smartphone handy? Can we use an old fashioned paper and pencil to do it in a long division style? At times, in everyday situations, we may face the task of having to figure the square root of a number.

Square root calculator