Find Squares of Numbers Ending with 5 in Seconds Using Vedic Maths – Part 1

If you are doing Geometry, Mensuration, or Algebra, you will mostly find the square of the number. It’s simple just to multiply the same number two times but solving the squares in an exam where speed and accuracy matter will take up much of your time.

Here at Vedic Math School, we teach Vedic maths to students who want to solve complex problems in their heads without feeling the need to lift the pen. Here in this Tutorial, we are going to teach you how to find squares of numbers ending with 5. Vedic Math School has brought you a trick from Vedic Maths to calculate the squares of numbers ending with 5 in mere seconds.

What does this mean by Numbers Ending with Five?

Look at numbers like 5, 15, 25, 65, 95, 105, 215, or 1025. Each of these numbers ends with five, or the unit place value of these numbers is 5. In this tutorial, we will learn how to find the square of all these numbers using Vedic maths.

You may be wondering, what about the other numbers that do not end with 5? So we discussed all these numbers in a separate tutorial. You can learn to find the square of any number here. This is also easy and equally applicable to all the numbers including Numbers Ending with Five.

Video Tutorial 

Whether you’re a watch-and-learn person or a read-and-savor type, we’ve got you covered. Check out the video tutorial titled.

 Scroll down and enjoy the written guide, because some of us like to be the boss of our own pace (no judgment, bookworms!). Either way, you’re just seconds away from mastering this topic…

Step-by-Step Process to Find the Square of Numbers that Ending with Five

Find the square of the number that ends with five and have a Three-step process. But you have to keep in mind this method is only applied when the unit place value is 5. Let’s Start…

Let’s understand this method better with an example. Let’s find the square of 65 with the help of this method.

Step 1: Square the number on the unit place, i.e. 5. Since we all know that the square of 5 is 25. We keep “25” aside for a while.

Step 2: Now in this step, we will deal with the number that is adjacent to the unit place. In this case, it’s 6.

We add 1 to 6 and then multiply the resultant number with the original number. In other words, we are going to plus one to the original number, 6 + 1 = 7, and then we are going to multiply the resultant number 7 with the original number i.e. 6. Therefore 6 x 7 = 42.

Step 3: Now, we will club step 1 and step 2 values together, not add, but club.

We got 42 from step 2 and we got 25 from step 1. We will proceed with clubbing them together and we got 4225. 

Therefore 4225 is the square of 65.

Understand with More Examples:

Example 1: Squaring 85 =?

1. Calculate the square of 5: 5 ^ 2 = 25
2. Focus on the left part: 8 + 1 = 9, 8 x 9 = 72
3. Club 72 and 25, 7225

So, 85^2= 7225

Example 2: Squaring 155 =?

1. Calculate the square of 5: 5 ^ 2 = 25
2. Focus on the left part: 15 + 1 = 16, 15 x 16 = 240
3. Club 240 and 25, 24025

So, 155^2=24025

Practice Questions

1. 145^2=?
2. 215^2=?
3. 75^2=?
4. 85^2=?
5. (5.35)^2=?
6. 195^2=?
7. 85^2=?
8. 995^2=?
9. 495^2=?
10. 965^2=?

For detailed solutions and explanations, make sure you check out the video lecture for free. 

Why Does This Trick Work?

This Vedic math trick works because of the way numbers ending with Five behave when squared. By breaking the problem into smaller parts, you get a manageable calculation that skips the need for traditional multiplication. And, adding “25” works consistently because of how numbers ending with Five relate to each other in multiplication.

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