Finding Square Roots

Updated May 8, 2019 | Infoplease 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!