Easiest Way to Find a Square Root
Easiest Way to Find a Square Root
Method 1 — Memorise perfect squares (fastest for 1–15)
Memorise: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225. These give instant whole-number answers.
Method 2 — Estimation (for any number)
Find the two perfect squares your number falls between. For √50: it is between √49=7 and √64=8. Estimate 7.1. Check: 7.1² = 50.41 (a little high). Try 7.07: 7.07² ≈ 49.98. So √50 ≈ 7.07.
Method 3 — Babylonian method (most accurate by hand)
x_new = (x + N/x) / 2
Start with any guess x. Apply the formula repeatedly until x stops changing. Example for √2: start x=1. Step 1: (1+2/1)/2=1.5. Step 2: (1.5+2/1.5)/2=1.4167. Step 3: (1.4167+2/1.4167)/2=1.4142. That is √2 to 4 decimal places in 3 steps.
Method 4 — Calculator (quickest)
Press √ on any calculator, or use this page. For spreadsheets: =SQRT(number) in Excel or Google Sheets.