Fastest and Easiest Way to Find the Square of any Number Ending in 5

Mathematics has its fair share of shortcuts and clever techniques — but some are so brilliant, they almost feel like magic. Today, I am going to share one of those tricks: how to quickly square any number ending in 5 in seconds — without a calculator.

Yes, you read that right. By the end of this post, you will be squaring numbers like 25, 65, or 95 faster than most people can even reach for their phones.

 

Here’s the simple, mind-blowing method:

Step 1: Take the first digit(s) of the number — everything before the 5.

Step 2: Multiply that number by the next higher number.

Step 3: Write 25 at the end.

Let's apply this technique to some examples.

Example 1: 25²

Solution

1. Take the first digit: 2.

2. Multiply it by the next number: 2 × 3 = 6.

3. Add 25 at the end: 625.

So: 25² = 625.

Example 2: 65²

Solution 

1. Take the first digit: 6.

2. Multiply it by the next number: 6 × 7 = 42.

3. Add 25 at the end: 4225.

So: 65² = 4225.

Example 3: 115²

Solution 

1. Take the first two digits: 11.

2. Multiply by the next number: 11 × 12 = 132.

3. Add 25 at the end: 13225.

So: 115² = 13225.

Why Does This Work? (The Math Behind the Magic)

Let’s break down what’s happening here with algebra:

A number ending in 5 can be written as:

n5 = 10n + 5

Squaring this:

(10n + 5)² = 100n² + 100n + 25 = 100n(n + 1) + 25

So the first part of the answer, n(n + 1), is the product of the number and its next higher number — and 25 always sits at the end. That’s why this trick works every single time.

Why This Trick Is So Useful

1. It’s lightning fast: Once you practice a bit, you’ll do these calculations in your head almost instantly.
2. It’s impressive: Imagine squaring 95² = 9025 before someone else even opens their calculator!
3. It builds mental math skills: This helps train your brain to spot patterns and think mathematically.

Challenge Yourself!

Try these without using a calculator:

1. 35² = ?

2. 85² = ?

3. 125² = ?

4. 175² = ?

Post your answers in the comments — let’s see how fast you get them!