The 2-Second Squaring Trick Textbooks Hide From You

how to square numbers ending in 5 instantly without a calculator. A lifesaver for Class 9 and 10 Mensuration.

Imagine you are solving a Surface Area and Volume question in your board exam. You plug the numbers into the formula, and suddenly you need to find the square of 45 (or 4.5).

The standard way? You stop, open your rough work page, write down 45 * 45, and start multiplying digit by digit. It takes 20 to 30 seconds of pure, boring calculation.

There is a legendary 2-second shortcut for this that completely eliminates rough work. If a number ends in 5, you can write down its square instantly using a simple two-step mental pattern.

How the Trick Works

Let’s take your example: 45²

Step 1: The Answer Always Ends in 25 Every single number ending in 5 will have a square that ends in 25. Write down 25 as the back half of your answer.

Step 2: Multiply the First Digit by the Next Number Look at the tens digit of 45, which is 4. Multiply 4 by the consecutive integer that comes right after it, which is 5.

• 4 * 5 = 20

Step 3: Combine Them Put the 20 in front of the 25.

• Answer = 2025

Why This Saves Your Board Exam

Think about how often you see decimals ending in 5 in Class 9 and 10 math.

• Need 35²? Take 3, multiply by 4 (3 * 4 = 12). The answer is 1225.
• Need 65²? Take 6, multiply by 7 (6 * 7 = 42). The answer is 4225.
• Need 95²? Take 9, multiply by 10 (9 * 10 = 90). The answer is 9025.

If you are dealing with a radius of 4.5 cm in a cone or cylinder question, you know 4.5 * 4.5 is just 20.25 without a single second of hesitation.

Textbooks make math look like a chore filled with long division and tedious multiplication lines. But math is actually just a game of patterns. Master the patterns, beat the clock, and save your energy for the conceptual problems!