Square numbers
Square any number ending in 5 in one step
Squaring 85 the long way is a full multiplication — but every number ending in 5 hides a fixed pattern.
Spot it when
The number ends in 5: 25, 35, 85, 125…
Watch it solved
direct way
25 × 25
long multiplication, carries, more steps
vedic cue
ends in 5
use 2 × 3, then append 25
Start with the square
The math problem is 25². A direct approach asks for 25 × 25; the Vedic shortcut notices that 25 ends in 5.
⚡ Speed Advantage
4× faster with Vedic Mathematics
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
A geometry problem needs the area of a 35 ft square plot, and you want it before reaching for the calculator.
3 × 4 = 12, tack on 25 → 1225.
Aptitude test: "Which is 85²?" with the clock running.
8 × 9 = 72, append 25 → 7225, faster than reading the options.
Building a quick squares table in your head for revision: 25, 35, 45, …
9 × 10 = 90, append 25 → 9025.
A three-digit one slips in — 125² in a number-system question.
Prefix 12 × 13 = 156, append 25 → 15625.
The method behind it
एकाधिकेन पूर्वेण
Ekadhikena Pūrveṇa
“By one more than the previous one”
When the last digit is 5, the prefix does all the work — multiply it by itself plus one.
via long multiplication (6+ steps, carrying).
, append (1 mental step).
Use when
- • Number ends in 5
- • Computing 1/(10n+9) recurring decimals
Avoid when
- • Numbers not ending in 5 (use Nikhilam or Urdhva instead)