Square Root Day only comes around once in a while, but your love for square roots can last all year—especially when you discover how cool they actually are! While most of us learned to press a button on the calculator to find square roots, there’s a whole world of tricks, patterns, and shortcuts that rarely make it into textbooks.
A numerical pun, Square Root Day celebrates the alignment of a date into the form of the squaring of a number. For example, May 5, 2025, or 5/5/25, represents 5 x 5 = 25, with the square root of 25 being five.
This May marks the only time a calendar has a Square Root Day in a 20-year span, with the last one being on April 4, 2016 and the next one on June 6, 2036. In fact, the day is so rare that it only occurs nine times within one century.
Here are 10 fun square root tricks that will surprise you, save you time, and maybe even impress your math teacher.
1. Perfect Squares End with Certain Digits
Did you know that perfect squares only end in 0, 1, 4, 5, 6, or 9?
That means if a number ends in 2, 3, 7, or 8—it can’t be a perfect square. Handy when estimating or checking your work.
2. The Last Digit of a Square Root Can Be Predicted
If a perfect square ends in 1, its square root ends in 1 or 9.
If it ends in 9, the root ends in 3 or 7.
This can help you narrow down square roots quickly, especially in mental math challenges.
3. Use Nearby Squares for Fast Estimation
Let’s say you want to estimate √50.
You know that √49 = 7 and √64 = 8, so √50 must be slightly more than 7.
This is great for quick approximations without a calculator.
4. Squaring Numbers That End in 5 Is Easy
This one’s magical:
Take any number ending in 5 (like 25 or 85), square it using this trick:
- Multiply the first digit(s) by the next higher digit
- Add 25 to the end
Example:
85² → 8 × 9 = 72 → add 25 → 7225.
Then take the square root of 7225, and you’re back at 85.
5. Use Prime Factorization to Find Square Roots
For smaller numbers, break them down into primes.
Example: √144 = √(2⁴ × 3²) = 2² × 3 = 12.
This helps visualize the math instead of relying on memorized answers.
6. You Can Estimate Square Roots With Averages
Here’s an old-school trick:
To estimate √N:
Pick a guess x, then average it with N/x.
Repeat a couple of times.
This is the Babylonian method and it converges fast!
Example: √10
1st guess: 3
(3 + 10/3) / 2 = 3.166
Try again: (3.166 + 10/3.166) / 2 ≈ 3.162
Pretty close!
7. Some Squares Have Repeating Root Patterns
1² = 1
11² = 121
111² = 12321
1111² = 1234321
See the pattern? It’s not magic—it’s math symmetry at work.
8. Square Roots of Small Decimals Are Easier Than You Think
√0.0004 = 0.02
Because √4 = 2, and then count half the decimal places.
√0.0009 = 0.03
This is useful when converting small measurements or probabilities.
9. Visualize Square Roots as Areas
A square root is just the side length of a square.
If a square has area 49 cm², each side is 7 cm.
Using this visual trick helps when solving word problems.
10. You Can Build Square Roots with LEGO Blocks
Seriously! Build perfect squares with LEGO or tiles—like 3×3, 4×4, 5×5 grids.
Then visually remove blocks and estimate side lengths to understand non-perfect square roots. Great for kids (and adults who like to play).
