How to square numbers ending in 5
Any number ending in 5 — 15, 65, 105, whatever — squares using a shortcut that skips multiplication almost entirely. Once it's automatic, questions like 85² stop being calculations and start being lookups.
The rule
Take the digit(s) before the 5 — call that number k. Multiply k by (k + 1). Then stick 25 on the end of that result. That's the whole answer.
Why it actually works
This isn't a coincidence or a memorized rule with no reason behind it — it falls straight out of algebra. A number ending in 5 can always be written as 10k + 5, where k is everything before the final digit. Squaring that:
(10k + 5)² = 100k² + 100k + 25
= 100k(k + 1) + 25
That last line is exactly the shortcut: k(k+1) gives the digits before the last two, and the +25 fills in the last two digits every time — because 100 times anything just shifts it two places left, and 25 slots in underneath.
Worked examples
15² — k = 1. 1 × 2 = 2. Append 25 → 225.
35² — k = 3. 3 × 4 = 12. Append 25 → 1225.
65² — k = 6. 6 × 7 = 42. Append 25 → 4225.
95² — k = 9. 9 × 10 = 90. Append 25 → 9025.
105² — k = 10. 10 × 11 = 110. Append 25 → 11025.
Notice the pattern holds the same way past 100 — k just becomes a two-digit number, and the method doesn't change at all.
Try it interactively
Pick a number and watch each step of the shortcut happen, then test yourself in the quiz below it.
A common mistake
The most common slip is forgetting the +25 has to occupy exactly two digits — for k×(k+1) values under 10, you still append "25" as two digits, not skip a place. 15² isn't "225" by accident of formatting — 1×2=2, and 2 followed by 25 is 225, which is correct specifically because 25 always takes the last two digit-slots.
Practice it for real
Once the pattern feels automatic on a few examples, drill it under a timer with random numbers — that's where it actually becomes fast recall instead of a rule you're re-deriving each time.