Squaring 2 Digit numbers in your head fast is easy and fun once you know these three simple steps that break it into three simple calculations. There is also two special cases where we can take a shortcut on the general method and get the result even faster and easier.

The two special cases are.

- Numbers Ending in 5
- Numbers Starting with 5

You can watch the video to see several examples for both the special cases and the general method for squaring any 2 digit numbers or continue reading if you prefer not to watch.

### 2 Digit Numbers Ending in 5

For these numbers because they end in 5 the last two digits of the result are always going to be 25. Knowing this means the only thing we need to work out is what the leading digits are going to be.

The formula to calculate the leading digits is:

*Multiply the tens digit by the next larger digit.*

What is "the next larger digit"? It is the digit you get when you add 1 to the digit you are looking at.

##### Examples

**75 squared**

As it ends in _5 we know the answer ends in _25 so we just need to calculate the leading digits.

The tens digit is 7, so we multiply it by the next larger digit, which is 8.

And there we have our leading digits, so the answer to our problem is:

**25 squared**

The tens digit is 2 so the next larger digit is 3 and we multiply them together.

So our leading digit is 6.

We know it ends in _25 so the answer to our problem is:

Now you know this little trick calculating the square of two-digit numbers ending in 5 should be easy to do in your head from now on.

### 2 Digit Numbers Starting with 5

The answer for two digit numbers starting with 5 can be calculated in two easy steps:

*Square the units digit.**Add 25 to the units digit.*

**Step 1 - Square the units digit.**

This step should always give us the last two digits of the result, so if we get only a single digit we put a leading zero to make up the two digits.

**Step 2 - Add 25 to the units digit.**

To get the leading digits of the result we simply add 25 to the units digit. Why 25, well that is the result of 5 squared.

Putting it all together:

Now we will move on to the General method for calculating the squares of any two digit number.

### Squaring Any 2 Digit Numbers

This general method of squaring two digit numbers will work for any of the two digit numbers, including those special cases mentioned above. There are three steps to the method:

*Square the units digit.**Multiply the two digits together then double the result.**Square the tens digit*

The easiest way to explain these steps is with an example, say 47 squared.

**Step 1 - Square the units digit.**

The units digit is 7.

So we would write 9, and we carry the 4

**Step 2 - Multiply the two digits together then double the result.**

We take the 4 and the 7 and simply multiply these two digits together and double the result.

We add the 4 we carried from step 1 to the 56.

We then write the 0 and carry the 6.

**Step 3 - Square the tens digit.**

The tens digit is 4, and we square this.

We add the 6 we carried from step 2 to the 16.

Write down the 22, and we have our result.

Once you know the rules then you should also be able to reverse direction and work the solution from left to right. This is better especially if you are doing the whole calculation mentally rather than writing it down as you go.

Lets reverse the order of the rules and work from left to right for .

**Reverse Step 1 - Square the tens digit.**

As the tens unit is 3 this means we are really looking at 30 so we will use 30 as we calculate as it will help to prevent us loosing our place in the answer.

**Reverse Step 2 - Multiply the two digits together then double the result.**

Again the 3 is 30 so we continue to use this as we work.

Adding the results of each step we get:

**Reverse Step 3 - Square the units digit.**

The units digit is 6 so we square this.

We add this to our running total.

So our answer is: .

There you have it a very easy way to calculate the square of a two digit number mentally.

So don't even think about reaching for that calculator the next time you need to find the square of a two digit number you should be able to mentally solve the problem before you even hit the calculator's "on" button.

For those of you who have read through the How to multiply double digit numbers may have felt a sense of déjà vu because it is the SAME METHOD! It is just described a little differently. What is squaring a 2 digit number? It is just multiplying a 2 digit number by itself.

GamerRomCom says

Math is such a sly minx, if you know the rules you’ll always be able to find ‘er.

As much work as it seems that memorizing these would be, it’s way easier than actually brute forcing your way though the numbers (you probably can’t unless you can really visualize a slide rule). Regardless it’s a great tool and probably a fun party trick too.

I’m going to pass this onto some math teachers I know.

Well done

*tips hat

Tony says

Hi Elliott,

Math is like that, you have to memorize the rules, but once you do you just just plug in the numbers and it will always work.

It is the simple “tricks” like these that those guys who are really good at math use but most other people just don’t know about. That is what this site is about trying to show that math does not have to be that hard.

Gwen Lorenzo says

thank you so much this method is way easier ….this helped me a lot in school.

Tony says

I am happy to hear you found this method helpful.