Finding Square Roots

Updated February 21, 2017 | Factmonster Staff

The easiest way to find a square root is to use a calculator, but you can do it without one. Here?s one way, using 12 as an example of the squared number:

  1. Pick a number that when squared, comes close to (but is less than) the number whose square root you?re finding: 3 3 = 9. This is a better choice than 4: 4 4 = 16
  2. Divide the number you?re finding the square root of (12) by the number you squared (3) in step 1: 12 3 = 4
  3. Average the closest square root (3) and the answer of step 2 (4): 3 + 4 = 7. 7 2 = 3.5
  4. Square the average to see how close the number is to 12:

3.5 3.5 = 12.25?Close, but not close enough!

Repeat steps 2 and 3 until the number squared is very close to 12:

Divide: 12 3.5 = 3.43

Average: 3.5 + 3.43 = 6.935

6.935 2 = 3.465

3.465 3.465 = 12.006, close enough!