Skip to Content

Log in / Sign up

wikiHow is where trusted research and expert knowledge come together. Learn why people trust wikiHow

How to Square Any Number

Download Article

Reviewed by Joseph Meyer

Last Updated: September 15, 2021 References

Download Article

When given a number to square, sometimes it's tough to find the square of the answer - especially when learning some of this intermediate to advanced math for the first time. It'll become second nature and easier later, but you may be thinking "this sounds complicated". No need to worry - it isn't that bad. This article below will explain this procedure.

Method 1

Method 1 of 2:

Using Traditional Squaring Methods

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/4\/47\/Square-Any-Number-Method-1-Step-1.png","bigUrl":"\/images\/thumb\/4\/47\/Square-Any-Number-Method-1-Step-1.png\/257px-Square-Any-Number-Method-1-Step-1.png","smallWidth":460,"smallHeight":746,"bigWidth":257,"bigHeight":417,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

1
Understand the meaning of squaring a number. When you square a number, you are essentially multiplying it by itself to form the product - or answer - to the multiplication problem. ^{[1]
X
Research source}
- Learn the common squares of numbers so you don't have to do them repetitiously over and over again. All of the following can be solved using the format given below, however, sometimes people should (or may want to) memorize these facts so they don't need to run these problem again.
  - $0^{{2}}=0\times 0=0$
  - $1^{{2}}=1\times 1=1$
  - $2^{{2}}=2\times 2=4$
  - $3^{{2}}=3\times 3=9$
  - $4^{{2}}=4\times 4=16$
  - $5^{{2}}=5\times 5=25$
  - $6^{{2}}=6\times 6=36$
  - $7^{{2}}=7\times 7=49$
  - $8^{{2}}=8\times 8=64$
  - $9^{{2}}=9\times 9=81$
  - $10^{{2}}=10\times 10=100$
  - $11^{{2}}=11\times 11=121$
  - $12^{{2}}=12\times 12=144$
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7a\/Square-Any-Number-Method-1-Step-2.png\/460px-Square-Any-Number-Method-1-Step-2.png","bigUrl":"\/images\/thumb\/7\/7a\/Square-Any-Number-Method-1-Step-2.png\/728px-Square-Any-Number-Method-1-Step-2.png","smallWidth":460,"smallHeight":191,"bigWidth":728,"bigHeight":303,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

2

Use pencil and paper to write down the number you'd like to square. Dependent on where the final answer will be needed, the first few times you may need a "practice" page.

Advertisement
{"smallUrl":"https:\/\/www.wikihow.com\/images\/2\/2a\/Square-Any-Number-Method-1-Step-3.png","bigUrl":"\/images\/thumb\/2\/2a\/Square-Any-Number-Method-1-Step-3.png\/326px-Square-Any-Number-Method-1-Step-3.png","smallWidth":460,"smallHeight":491,"bigWidth":326,"bigHeight":348,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

3
Write the same number below and expect to multiply them. If you need help, wikiHow has a guide on that too . Write number under number.
- Expect mistakes the first several times you end up having to use multiplication.
{"smallUrl":"https:\/\/www.wikihow.com\/images\/8\/8a\/Square-Any-Number-Method-1-Step-4.png","bigUrl":"\/images\/thumb\/8\/8a\/Square-Any-Number-Method-1-Step-4.png\/299px-Square-Any-Number-Method-1-Step-4.png","smallWidth":460,"smallHeight":678,"bigWidth":299,"bigHeight":441,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

4

Multiply these numbers (called factors) using the format explained above. This type of multiplication solution solving is considered to have been solved using long multiplication . ^{[2]
X
Research source}

Advertisement

Method 2

Method 2 of 2:

Utilizing Difference of Perfect Squares

Download Article

{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/8\/84\/Square-Any-Number-Method-2-Step-1.png\/460px-Square-Any-Number-Method-2-Step-1.png","bigUrl":"\/images\/thumb\/8\/84\/Square-Any-Number-Method-2-Step-1.png\/516px-Square-Any-Number-Method-2-Step-1.png","smallWidth":460,"smallHeight":222,"bigWidth":516,"bigHeight":249,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

1

Understand the difference of perfect squares shortcut. Shortcut to and write down the quick solution. Write down this trigger shortcut. The difference of two perfect squares states that when two squares are subtracted by one another the product of that number and another number when added (then subtracted) will equal your answer. This can be shown as $x^{2}-p^{2}=(x+p)(x-p)$ . ^{[3]
X
Research source}
2
Find the value of $x^{2}$ . Evaluate what you know. Place the x value into the "equation" and add $p^{2}$ to both sides (cancels on the left side) will yield $x^{2}=(x+p)(x-p)+p^{2}$ . Doing so, you'll be able to set up to capture your answer. ^{[4]
X
Research source
Great Courses video series: Secrets of Mental Math, Episode 11:Advanced Mathematics} ^{[5]
X
Research source}

{"smallUrl":"https:\/\/www.wikihow.com\/images\/2\/29\/Square-Any-Number-Method-2-Step-2.png","bigUrl":"\/images\/thumb\/2\/29\/Square-Any-Number-Method-2-Step-2.png\/381px-Square-Any-Number-Method-2-Step-2.png","smallWidth":460,"smallHeight":338,"bigWidth":381,"bigHeight":280,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}
- Build your factors and insert the values of the item you'd like to square into the formatted equation. Let x equal the number you'd like to find. Insert the number anywhere x is shown.
- Think about a number you could later insert for the p value. Consider making things easy and ensure the x value can be rounded up to the nearest 5 units, however, rounding it will work to any possible number. You don't want to think too far from the number.
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/78\/Square-Any-Number-Method-2-Step-3.png\/460px-Square-Any-Number-Method-2-Step-3.png","bigUrl":"\/images\/thumb\/7\/78\/Square-Any-Number-Method-2-Step-3.png\/651px-Square-Any-Number-Method-2-Step-3.png","smallWidth":460,"smallHeight":281,"bigWidth":651,"bigHeight":397,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

3

Insert this number that you can add that will bring you into these common factor numbers into the p value in the equation. ^{[6]
X
Research source}
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/2f\/Square-Any-Number-Method-2-Step-4.png\/460px-Square-Any-Number-Method-2-Step-4.png","bigUrl":"\/images\/thumb\/2\/2f\/Square-Any-Number-Method-2-Step-4.png\/555px-Square-Any-Number-Method-2-Step-4.png","smallWidth":460,"smallHeight":344,"bigWidth":555,"bigHeight":415,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

4

Evaluate the much-smaller $p^{2}$ answer and add it to the equation in the place of the variable p.
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/af\/Square-Any-Number-Method-2-Step-5.png\/460px-Square-Any-Number-Method-2-Step-5.png","bigUrl":"\/images\/thumb\/a\/af\/Square-Any-Number-Method-2-Step-5.png\/572px-Square-Any-Number-Method-2-Step-5.png","smallWidth":460,"smallHeight":397,"bigWidth":572,"bigHeight":494,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

5

Evaluate the equation. Add the x and p values, as well as subtracting them as the equation explains, then multiply those numbers together to get your product so far. Find the product to this part of the equation. ^{[7]
X
Research source}
{"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/4f\/Square-Any-Number-Method-2-Step-6.png\/460px-Square-Any-Number-Method-2-Step-6.png","bigUrl":"\/images\/thumb\/4\/4f\/Square-Any-Number-Method-2-Step-6.png\/575px-Square-Any-Number-Method-2-Step-6.png","smallWidth":460,"smallHeight":426,"bigWidth":575,"bigHeight":533,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/en.wikipedia.org\/wiki\/Fair_use\">Fair Use<\/a> (screenshot)<br>\n<\/p><\/div>"}

6

Add the product to this squared product for p. Find the sum of these two numbers. The sum will be the answer to the number squared. ^{[8]
X
Research source}

Advertisement

Community Q&A

Search

Add New Question

Question

What is the square of 3?

Community Answer

3² = (3)(3) = 9.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 0 Helpful 0
Question

What if you're squaring a negative number?

Community Answer

To square a negative number, multiply it by itself (just as you would with a positive number). For example, (-4)² = (-4)(-4) = +16. (Anytime a negative number is multiplied by another negative number, the product is positive.)

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 0 Helpful 0
Question

How do you square numbers with a decimal point (like 17.45)?

Community Answer

Multiply the number by itself, and then place the decimal point by counting the total number of digits to the right of the decimal point in both of the numbers. For example, (1745)(1745) = 3045025. There are two digits to the right of the decimal point in 17.45, for a total of four digits in the two numbers. So the decimal point in the answer is placed four digits to the left of the right-most digit: 304.5025.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 0 Helpful 0

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Advertisement

Tips

Submit a Tip

All tip submissions are carefully reviewed before being published

Thanks for submitting a tip for review!

You Might Also Like

Advertisement

References

About This Article

Reviewed by:

Math Teacher

This article was reviewed by Joseph Meyer . Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. This article has been viewed 29,265 times.

22 votes - 42%

Co-authors: 4

Updated: September 15, 2021

Views: 29,265

Categories: Mathematics

Thanks to all authors for creating a page that has been read 29,265 times.

Reader Success Stories

Jackson Ray

Jun 17, 2021

"How to square numbers by using the area formula.(cirlces)."

Share your story

Did this article help you?

Advertisement

X

-

-

539

.mwimg a.image{display:none}#header_logo{display:none}#cse-search-box{display:none}#cse-search-box-noscript{display:block !important}#cse-search-box-noscript .cse_q{color:#FFF;background-color:#B3CE9C}.wh_search .cse_q{width:88%}#mw-mf-main-menu-button{display:none;visibility:hidden}.header .search{display:none}#search_footer .cse_sa{background-image:url(/extensions/wikihow/mobile/images/white_mag.png);background-size:22px}.related_box{display:block;background:#EEE;border:5px solid #FFF;vertical-align:bottom;width:127px;background-size:180px;float:left;height:120px;position:relative}.related_box p{line-height:15px !important;font-size:13px;background-color:rgba(67,95,44,.4);color:#FFF;font-weight:bold;padding:8px;margin:0 !important;position:absolute;bottom:0}#noscript_header_logo{display:table-cell;vertical-align:middle;background-position:50% 77%;background-repeat:no-repeat;background-image:url(/extensions/wikihow/mobile/images/wikihow_logo_230.png);background-size:105px;width:auto;height:51px;padding:0 14px}.articleinfo{display:none}#iorg_free_data{z-index:50;width:100%;position:fixed}#ara_recommendations{display:none}

Design a Mobile Website

View Site in Mobile | Classic

Share by: