For example, the square root of 1 is 1 because 1 multiplied by 1 equals 1 (1X1=1). However, the square root of 4 is 2 because 2 multiplied by 2 equals 4 (2X2=4). Think of the square root concept by imagining a tree. A tree grows from an acorn. Thus, it’s bigger than but related to the acorn, which was at its root. In the above example, 4 is the tree, and 2 is the acorn. Thus, the square root of 9 is 3 (3X3=9), of 16 is 4 (4X4=16), of 25 is 5 (5X5=25), of 36 is 6 (6X6=36), of 49 is 7 (7X7=49), or 64 is 8 (8X8=64), of 81 is 9 (9X9=81), and of 100 is 10 (10X10=100). [3] X Research source
For example: 16 divided by 4 is 4. And 4 divided by 2 is 2, and so on. Thus, in those examples, 4 is the square root of 16, and 2 is the square root of 4. Perfect square roots do not have fractions or decimals because they involve whole numbers.
N equals the number whose square root you are trying to find. It goes inside the check mark symbol. [5] X Research source Thus, if you are trying to find the square root of 9, you should write a formula that puts the “N” (9) inside the check mark symbol (the “radical”) and then present an equal sign and the 3. This means the “square root of 9 equals 3. ”
Let’s say you want to find the square root of 20. You know that 16 is a perfect square with a square root of 4 (4X4=16). Similarly, 25 has a square root of 5 (5X5=25), so the square root of 20 must fall in between 4 and 5. You could guess that 20’s square root is 4. 5. Now, simply square 4. 5 to check your guess. That means you multiply it by itself: 4. 5X4. 5. See if the answer is above or below 20. If the guess seems off, simply try another guess (maybe 4. 6 or 4. 4) and refine your guess until you hit 20. [6] X Research source For example, 4. 5X4. 5 = 20. 25, so logically you should try a smaller number, probably 4. 4. 4. 4X4. 4 = 19. 36. Thus, the square root of 20 must lie in between 4. 5 and 4. 4. How about 4. 445X4. 445. That’s 19. 758. It’s closer. If you keep trying different numbers using this process, you will eventually get to 4. 475X4. 475 = 20. 03. Rounding off, that’s 20.
Then, divide your number by one of those square root numbers. Take the answer, and find the average of it and the number you divided by (average is just the sum of those two numbers divided by two). Then take the original number and divide it by the average you got. Finally, find the average of that answer with the first average you got. Sound complicated? It can be easiest to follow an example. For example, 10 lies in between the 2 perfect square numbers of 9 (3X3=9) and 16 (4X4=16). The square roots of those numbers are 3 and 4. So, divide 10 by the first number, 3. You will get 3. 33. Now, average the 3 and 3. 33 by adding them together and dividing them by 2. You will get 3. 1667. Now take 10 divided by 3. 1667. The answer is 3. 1579. Now, average 3. 1579 and 3. 1667 by adding them together and dividing the sum you get by two. You will get 3. 1623. Check your work by multiplying your answer (in this case 3. 1623) by itself. Indeed, 3. 1623 multiplied by 3. 1623 equals 10. 001.
