Find square of a number within few seconds

Eight Standard >> Find square of a number within few seconds

How to Find the Square of 2 or 3-Digit Numbers in Seconds – Tricks and Examples

Finding the square of a number is a common task in many competitive exams, mental math challenges, or everyday calculations. Doing it quickly and accurately can save valuable time. In this article, we’ll explore easy tricks to find the square of two-digit and three-digit numbers within seconds, along with examples and explanations. With regular practice, these mental math methods can become second nature.

Why Learn Squaring Tricks?

Saves time in exams and interviews.
Improves mental calculation speed.
Helps in understanding number patterns.

Method 1: Using the Identity (a ± b)² = a² ± 2ab + b²

This method works best when the number is close to a base like 10, 50, or 100.

Example 1: Square of 48

48 is close to 50. Let’s write it as (50 - 2)

(50 - 2)² = 50² - 2 × 50 × 2 + 2²
= 2500 - 200 + 4 = 2304

Method 2: Using the Formula (ab)² = a² × 100 + 2ab × 10 + b²

This is useful for two-digit numbers where a is the tens digit and b is the units digit.

Example 2: Square of 23

In this case, a = 2 and b = 3
23² = 2² × 100 + 2 × 2 × 3 × 10 + 3²
= 400 + 120 + 9 = 529

Method 3: For Numbers Ending in 5

Any number ending in 5 can be squared using:
(n5)² = n × (n+1) × 100 + 25

Example 3: Square of 85

n = 8
85² = 8 × 9 × 100 + 25 = 7225

Method 4: Square of 3-Digit Numbers Close to 100 or 1000

Example 4: Square of 103

103 is near 100, so:
(100 + 3)² = 100² + 2 × 100 × 3 + 3²
= 10000 + 600 + 9 = 10609

Tips to Master These Tricks:

Work on squaring numbers that are close to 50, 100, or 1000.
Memorize squares from 1 to 30 for speed.
Write the identities on a note card to review regularly.

Learn With Video

If you're a visual learner, be sure to check out the video tutorial where these tricks are explained step by step with animations and voice guidance.

By applying these mental math tricks, you can square two- or three-digit numbers in just seconds — without a calculator! Whether you’re preparing for exams or sharpening your brain, regular practice with these methods will boost your speed and accuracy.