|

# Finding Square Roots

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!

 Table of Squares and Square Roots Numbers and Formulas Scientific Notation

#### More on Finding Square Roots from Infoplease:

Related content from HighBeam Research on: Finding Square Roots

Square Roots (Mathematics Teaching)

A Unification of Ensemble Square Root Kalman Filters (Monthly Weather Review)

Emitter Location: reporting Location accuracy.(reports on military electronics)(root-mean-square) (Journal of Electronic Defense)

The Square Root of Queer (American Theatre)

The Square Root of Roundtables (Folio: the Magazine for Magazine Management)

Visualising the Complex Roots of Quadratic Equations with Real Coefficients (Australian Senior Mathematics Journal)

Opaque Square (Australian Mathematics Teacher)

Computing quaternionic roots by Newton's method. (Electronic Transactions on Numerical Analysis)

Finding Volumes between a Quadric Surface and a Plane (Electronic Journal of Mathematics and Technology)

# 24 X 7

## Private Tutor

 24 x 7 Tutor Availability Unlimited Online Tutoring 1-on-1 Tutoring