Squaring Numbers Ending in 5: A 10-Second Vedic Trick

The Pattern Behind the Trick

Any number ending in 5 can be written as 10a + 5, where a is the digit (or digits) in front of the 5. Squaring (10a + 5)² algebraically expands to 100a(a + 1) + 25 — which means the answer always ends in 25, and the digits before that are simply a × (a + 1).

The Rule in Two Steps

• Take the digit(s) before the 5 — call this number a — and multiply it by the next whole number, a + 1.
• Write "25" right after that product. That's your answer.

Worked Example

65²

1. The digit before 5 is a = 6
2. Multiply by the next number: 6 × 7 = 42
3. Attach 25: 4225

Another Worked Example

85²

1. a = 8
2. 8 × 9 = 72
3. Attach 25: 7225

It Works for Bigger Numbers Too

105²

1. a = 10 (everything before the final 5)
2. 10 × 11 = 110
3. Attach 25: 11025

25²

1. a = 2
2. 2 × 3 = 6
3. Attach 25: 625

Why It's Reliable

Because this comes directly from algebra rather than a memorized shortcut, it works for every number ending in 5 — two-digit, three-digit, or beyond. The only "calculation" you ever do is a × (a + 1), which is one multiplication of consecutive integers, usually easy to do in your head.

Practice Tip

Write down five numbers ending in 5 — say 15, 35, 45, 75, 95 — and square each one using this method before checking with a calculator. Once a × (a + 1) becomes instant for small values of a, the whole trick takes under ten seconds per question, which is exactly why it's such a favourite for timed arithmetic sections.

Keep a mental list of a × (a + 1) results for a = 1 to 12 handy while practicing; recognizing them instantly is what turns this from a trick into genuine speed.