A Math Trick for Squaring Two Digit Numbers

(Last Updated On: June 1, 2018)

A Math Trick for Squaring Two Digit Numbers
If you’ve ever been faced with squaring numbers, you know that once you get beyond the single digits, the outcome is a product that is pretty large. And just seeing the answer likely makes you cringe, as you think, “how could I possible do that without a calculator?”

Well here’s the thing – you actually can! All you have to do is memorize these 4 steps below. It might take a little practice for you to get used to the process and to know which number is which as part of the equation, but once you get it all down pat, you’ll be a squaring whiz.

Ready to give it a try? Here’s a math trick for squaring two digit numbers:

Steps for Squaring Two Digit Numbers

Let’s say for example, that you are trying to square 32. Follow these steps (see the values below):

Step 1: Add the last digit of the number you are trying to square to the entire number itself, creating your sum.
Step 2: Multiply the sum (step 1) by the first digit of the base number.
Step 3: Square the last digit of the base number.
Step 4: Append the square number (step 3) to the product calculated above (step 2).

For example: 32²
Base number: 32     First digit: 3      Last digit: 2

Step 1: 2 + 32 = 34
Step 2: 34 x 3 = 102
Step 3:  = 4
Step 4: 1024

Let’s try one more example. How about 21²?
Base number: 21      First digit: 2      Last digit: 1

Step 1: 1 + 21 = 22
Step 2: 22 x 2 = 44
Step 3:  = 1
Step 4: 441

Tackling Double Digits

But what if the square number is double digit? If you calculate the squared value in step 3 and the result is a double-digit number, don’t fret. Just like when you were in elementary school, you have to carry the one, and add it on!

Here is another example: 69²
Base number: 69      First digit: 6      Last digit: 9

Step 1: 9 + 69 = 78
Step 2: 78 x 6 = 468
Step 3:  = 81
Step 4: 4,761 (where the 8 and 8 are added together, and the 1 is carried over to the digit before. Essentially, the problem becomes 4,680 + 81)

How about 17²?
Base number: 17      First digit: 1      Last digit: 7

Step 1: 7 + 17 = 24
Step 2: 24 x 1 = 24
Step 3:  = 49
Step 4: 289 (240 + 49)

Grab a piece of paper and pencil and practice a few to get the hang of the steps. Admittedly, it might take some time to really get the hang of it. Eventually though, hopefully you can ditch the paper and put your mental math skills to work. Before long, you just might become an expert at squaring two digit numbers in your head!

Think you have got the hang of it? If so, test your knowledge of squaring two digit numbers in the quiz below. And make sure to check out our other Math Trick blog posts.

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