The Magical Trick for Squaring Numbers Ending in 5!

Hello, Young Math Wizards! ✨

Are you ready to learn a fun and easy trick for squaring numbers that end in 5? This trick will help you get the answer quickly and understand why it works. Let’s jump in!

The Cool Trick

When you want to square a number ending in 5, like 45 or 75, here’s a super easy trick:

Steps of the Trick

1. Look at the Number: Take a number ending in 5. For example, 45.
2. Remove the 5: Focus on the number before 5. So for 45, you focus on 4.
3. Find the Next Number: The number right after 4 is 5.
4. Multiply Them: Multiply 4 by 5. You get 20.
5. Add 25: Add 25 to the end of 20 to get 2025.

Why Does This Trick Work?

Let’s break it down with a simple explanation:

Understanding the Numbers:

When you square a number like 45, it’s the same as multiplying 45 by itself: 45 × 45.

To make this easier, we use a special trick that involves the number before the 5 and the number right after it.

Why Multiply 4 by 5?

Think of 45 as 40 + 5. When we square it, we’re actually calculating (40 + 5) × (40 + 5).

To do this, we break it into parts:

• Multiply the 40s: 40 × 40 = 1600
• Multiply 40 by 5 and 5 by 40: 40 × 5 + 5 × 40 = 200 + 200 = 400
• And then, 5 × 5 = 25

So, when we multiply 4 (from 40) by 5, it’s like finding part of the 400. The 4 and 5 give us the middle part of the answer, and 25 is the part that always ends the answer because squaring any number ending in 5 always ends in 25!

Putting It All Together:

• Multiplying the 4 by the next number (5) gives us the middle number we need.
• Adding 25 at the end gives us the correct final part because every squared number ending in 5 ends with 25.

Visualizing the Trick

Let’s imagine you have a box of 45 candy pieces. If you want to figure out how many candies you have in a square arrangement, you can use this trick:

Imagine arranging the candies in rows. When you multiply the number before 5 (4) by the next number (5), you’re figuring out how many rows and columns fit.

The 25 candies at the end are like the extra candies that always show up when squaring numbers ending in 5.

Fun Examples

Example 1: 35 Squared

• Number: 35
• Remove 5: Focus on 3
• Next Number: 4
• Multiply: 3 times 4 equals 12
• Add 25: 12 becomes 1225

So, 35² = 1225.

Example 2: 125 Squared

• Number: 125
• Remove 5: Focus on 12
• Next Number: 13
• Multiply: 12 times 13 equals 156
• Add 25: 156 becomes 15625

So, 125² = 15625.

Try It Out Yourself!

Want to see this magic trick in action? Use our interactive canvas to:

1. Enter a Number: Type a number ending in 5.
2. Watch the Trick: See each step of the trick.
3. Check Your Answer: Find out if you got it right!