Square Any Number Ending in 5 in Just 5 Seconds!

Have you ever wondered how some people can calculate numbers like 35² = 1225 or 95² = 9025 almost instantly?

Here's a simple trick that every Class 8–10 student should know.

The Magic Rule

For any number ending in 5:

Step 1:

Take the digit(s) before the 5.

Step 2:

Multiply that number by its next consecutive number.

Step 3:

Write 25 at the end.

That's it!

Example 1: 35²

The number before 5 is 3.

Multiply 3 × 4 = 12

Now attach 25.

35² = 1225

Example 2: 65²

The number before 5 is 6.

Multiply 6 × 7 = 42

Attach 25.

65² = 4225

Example 3: 95²

The number before 5 is 9.

Multiply 9 × 10 = 90

Attach 25.

95² = 9025

Example 4: 115²

The number before 5 is 11.

Multiply 11 × 12 = 132

Attach 25.

115² = 13225

But Why Does This Work?

Let's look at 35².

We can write 35 as:

35 = 10 × 3 + 5

So,

(10n+5)2=100n(n+1)+25(10n+5)^2=100n(n+1)+25(10n+5)2=100n(n+1)+25

This means:

• Multiply the number before 5 (n) by the next number (n+1)
• Then place 25 at the end

Exactly the shortcut we used!

Try These Yourself

Without using a calculator, find:

1. 25²
2. 75²
3. 125²
4. 205²

Answers

25² = 625

75² = 5625

125² = 15625

205² = 42025