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An Easy Math Trick to Mentally Square Numbers Ending 5

Updated on February 6, 2013

Square of 5

Square of 5
Square of 5 | Source

What is a Square?

A square when referring to number in math comes from the geometric term square.

The square of 2 or a square with sides of 2. Is 2 to the power of 2 or 2 x 2 or 4


There are several way of notating a square

2^2 would notate the square

2 x 2 is a number sentence that represents the square.


A square of 5 would look like the images to the right side of the screen.


Imagine that you have a square with sides of 5. A squares sides are all the same so you would only have to notate the single 5 on one side. In order to find the area you would have multiply 5 by 5 or find the square of 5.


There are many tricks and patterns throughout math. This easy trick will help you do mental math for the squares of numbers ending in the digit 5 for all numbers that are greater than 5.


Squaring Numbers Ending in 5

There are many tricks to multiplying and squaring numbers.


This ones is easier than is looks.


Lets Start with what we know. We know the 5 squared or 5 times 5 is 25. This is a simple basic fact that you should already have memorized. If you don't know your basic facts, learn them! This is one thing I feel strongly about in math, if you don't know your facts math will always remain hard and out of reach.


This trick will work for every one after 5.

15, 25, 35, 45, 55, and so on.

Let us look at the first example.



Finding the Square of 35

Find the square of 35
Find the square of 35 | Source

Finding the square of 35

The first example is of the number 35.

The three is the digit we need to find the square. The five is going to be ignored. We already know 5 times 5 is 25 so all the numbers will be ending in the number 25. We are going to tack these digits onto the back end of the digits that this trick finds.

We need the digits in front of the 5 in order to make the trick work.

The digit(s) in front of the 5 for this problem is 3.

We need 3 and one more than 3.


We are going to multiply 3 by (3 +1)

3 x 4 =12

Then we tack 25 onto the end

to get 1225.

The square of 35 is 1225.


The square of 75

Square of 75
Square of 75 | Source

Square of 75

The same concept applies here

The digits before the 5 is 7. We need 7 and 1 more than 7.

7 times 8 equals 56.

56 tack on 25

5625.


One final example of Squaring a 5 Number

Just to make sure this pattern continues we are going to try a multi digit numbers and calculate the same thing.

135 is the number I am going to use for this.

I am using this number because it has more than one digit in front of the 5 to show that this pattern continues to work.

Example of the Square

Square of 135
Square of 135 | Source

Patterns in Math

If you write out the squares you will see something like this:

25

225

625

1225

2025

3035

4225

5625

7225

and so on.


See if you can find the patterns in other squares that will help you be faster and more effective in math.


Test Yourself


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    • NornsMercy profile image

      Chace 4 years ago from Charlotte, NC

      This is awesome! I'm terrible at math so it feels like my brain just re-wired itself in a big way after reading this...

    • aa lite profile image

      aa lite 4 years ago from London

      That is a very cool trick! I wonder why it works. My brain is too tired to think about it, so I guess I will go on wondering for a while still.

    • kingkos profile image

      kingkos 4 years ago

      Nice tips in mathematics, I want students see this article to know the trick in square numbers. Nice hub!