Fast squaring of numbers ending in 5

Of all the mental math shortcuts, this is probably the fastest one to master — and the one that surprises people most. Any number ending in 5 can be squared in two steps, with zero guesswork about carrying or rounding.

The rule

Write the number as 10a + 5, where a is the leading digit(s) before the 5. Then:

In plain steps:

• Take the digit(s) before the 5, call it a
• Multiply a by (a + 1)
• Write 25 directly after that result

That's the entire method. No rounding, no correction term — just two numbers placed next to each other.

Worked example: 35²

Here a = 3 (everything before the 5).

• a × (a + 1) = 3 × 4 = 12
• Place 25 after it

Worked example: 85²

Here a = 8.

• a × (a + 1) = 8 × 9 = 72
• Place 25 after it

Why it works

This is the same base-and-deviation identity behind most squaring shortcuts, just simplified because the units digit is fixed at 5. Expanding (10a + 5)² algebraically gives 100a² + 100a + 25, which factors into 100 × a(a+1) + 25 — exactly the two-step rule above. The units digit being fixed is what removes the need for any correction step at all.

It scales past two digits

The same rule works for three-digit numbers ending in 5. For 125², a = 12:

• a × (a + 1) = 12 × 13 = 156
• Place 25 after it

The only extra work is that a × (a+1) itself gets bigger — the placement rule never changes.

Where this actually helps

Numbers ending in 5 come up constantly in percentage calculations, average-based questions, and approximation-heavy DI sets. Being able to square 45 or 95 instantly — without the multi-step base-100 method — is a small but very frequent time save across a timed paper.