Content

• Steps
• Advice

You can easily find the square root of a number if the number is an integer. If the number is not whole, you can logically deduce the method below to find the square root of any number, even if you don't have a calculator. You will need to know how to use simple multiplication, addition, and division to do this.

Steps

Method 1 of 3: Find the square root of the integer

1. 

   Find the square root by multiplying. The square root of a number is the number that, when you multiply that number by itself, you will find the first number you have. Think of it this way: "What number can you multiply by itself to get the number you already have?"
   • For example, the square root of 1 is 1 because 1 times 1 equals 1 (1X1 = 1). However, the square root of 4 is 2 because 2 times 2 equals 4 (2X2 = 4). Imagine the concept of a square root like a tree. Plants sprout from oak seeds. So even though the tree is larger than the seed, the tree is still related to the seed since the seed is the base of the plant. In the above example, 4 is a tree and 2 is an oak seed.
   • So the square root of 9 is 3, of 16 is 4 (4X4 = 16), of 25 is 5 (5X5 = 25), of 36 is 6 (6X6 = 36), of 49 is 7 (7X7 = 49) , of 64 is 8 (8X8 = 64), of 81 is 9 (9X9 = 81), and of 100 is 10 (10X10 = 100).

2. 

   
   
   Use division to find the square root. To find the square root of an integer, you can divide the integer by the numbers in turn until you find a quotient that is exactly the same as your divisor.
   • Example: 16 divided by 4 equals 4. 4 divided by 2 equals 2, and so on. So in the example above, 4 is the square root of 16, and 2 is the square root of 4.
   • Square numbers are not fractions or decimals because they are the square root of the whole number.

3. 

   
   
   Use the correct symbols for the square root. Mathematicians use a special symbol called the radical sign to write the square root. This mark will look like a tick connected to a horizontal line.
   • N is the number for which you are looking for the square root. N will be in the radical sign.
   • So if you're trying to find the square root of 9, your formula will have N (9) in the root, then the equal sign, and the number 3. This formula means "the square root of 9 equals 3. . "
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Method 2 of 3: Find the square root of other numbers

1. 

   
   
   Guess then use the exclusion method. It is harder to find the square root of an integer, however, this doesn't mean you can't.
   • For example, you want to find the square root of 20. You already know that 16 is a perfect square with the square root of 4 (4X4 = 16). And 25 also has the square root of 5 (5X5 = 25), so the square root of 20 would be in that range.
   • You can guess that the square root of 20 is 4.5. Now, square 4,5 to verify your prediction. That is, you multiply 4.5 by itself: 4,5X4,5. Notice if your answer is greater than or less than 20. After that, continue multiplying as predicted (4.6 if the result is greater than 20 or 4.4 if less than 20) and continue to predict until when you get 20.
   • For example, 4,5X4,5 = 20,25, theoretically you should try a smaller number, maybe 4.4. 4.4X4.4 = 19.36. So the square root of 20 would be between 4.5 and 4.4. Try 4,445X4,445. The answer is 19,758. That is closer to 20 already. If you keep trying different numbers with the method, you will end up with 4,475X4,475 = 20.03. When you round down, the answer is 20.

2. 

   Use the average method. With this method, you will start by finding two integers closest to your square root.
   • Then, divide the number you currently have by those square roots. Find the average of the quotient you just found with the corresponding divisor (the arithmetic mean is the sum of two numbers divided by two). Then, divide your divided number by the average above. Then, find the average of the answers you just divided.
   • Sound troublesome, right? The following is an illustrative example. For example, 10 is between two square numbers 9 (3X3 = 9) and 16 (4X4 = 16). The square root of these two numbers is 3 and 4. Divide 10 by the first number, 3. You will get 3.33. Now, you find the average of 3 and 3.33 by finding their sum and dividing the sum by 2. You will get 3.1667. Now divide 10 by 3.1667. The answer is 3,1579. Find the mean of 3,1579 and 3,1667 by adding them together and dividing the sum by 2. Your final answer is 3.1623.
   • Check the results by multiplying your answer (in this case, 3,1623) by itself. 3.1623 multiplied 3.1623 equals 10,001.
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Method 3 of 3: Square negative numbers

1. 

   Squeeze negative numbers in the same way as above. Remember that a negative number multiplied by a negative number produces a positive number. So, the square of a negative number is a positive number.
   • For example, -5X-5 = 25. But 5X5 = 25. Remember that the square root of 25 can be -5 or 5. That means there are 2 different square roots for a number.
   • Similarly, 3X3 = 9 and -3X-3 = 9, so the square root of 9 is both 3 and -3. Positive numbers are usually the main solution, so you just need to pay attention to this answer.

2. 

   Use the computer. You should know how to do the math by hand, but there are plenty of tools out there that are dedicated to finding square roots.
   • Find the root mark on the calculator.
   • The online calculator will ask you to enter the number you want to find the square root of and click on a button. The calculator will then find the square root of that number.
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Advice

• Remember the first few squares in the multiplication table:
  • 0 = 0, 1 = 1, 3 = 9, 4 = 16, 5 = 25, 6 = 36, 7 = 49, 8 = 64, 9 = 81, 10 = 100,
  • And also slowly remember these spells: 11 = 121, 12 = 144, 13 169, 14 = 196, 15 = 225, 16 = 256, 17 = 289 ...
  • From the simple squares above, apply to the following squares: 10 = 100, 20 = 400, 30 = 900, 40 = 1600, 50 = 2500, ...