ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

squaring maths trick how to quickly square a number that ends in 5 e.g. 35 squared.

Updated on February 14, 2011

First an example.

You need to compute 35 x 35.

Instantly, a child can answer "3 x 4 = 12 so 35 squared is 1,225"

Now the trick is explained

The number must end in 5,  although numbers over 99 are a little harder, and as they get larger it gets harder. Even so, it's a useful trick for small numbers.

Given 45 x 45, you take the 4 and multiply it by (4+1). i.e. 4 * 5 = 20, then you tac on 25 at the end to give 2025.

If the number is 115 squared, then you do 11 x 12 and tac on 25. So 115 squared = 13,225.

Some more examples

N       n squared     the trick

5       25            0
15      225           2
25      625           6
35      1225          12
45      2025          20
55      3025          30
65      4225          42
75      5625          56
85      7225          72
95      9025          90
105     11025         110
115     13225         132
125     15625         156
135     18225         182
145     21025         210
155     24025         240
165     27225         272
175     30625         306
185     34225         342
195     38025         380
205     42025         420
215     46225         462
225     50625         506
235     55225         552
245     60025         600

Why does this work?

You can use some algebra to see why this works.

Our number ends in 5 and so can be written:


Where X is all the digits to the left of the 5 so that X can represent 16 in X5 for 165.

We can temporarily forget the actual value of x and try to work out the formula for X5 squared.

Since X is in the 10s column, then we can rewrite X5 as (10x+5).

Let's find (10x+5) squared.

= (10x+5)(10x+5)

= 100xx + 50x + 50x + 25

= 100xx + 100x +25

take out the 100x common to the first two terms...

= 100x(x+1) + 25


We have our formula. Take the x and multiply by (x+1) and make this 100 times bigger and add 25.

See also:


    0 of 8192 characters used
    Post Comment

    • profile image

      marcello 3 years ago

      I still don't understand your explanation.

    • Manna in the wild profile image

      Manna in the wild 7 years ago from Australia

      Yes those would be trigonometric identities or series expansions.

    • profile image

      Kirui 7 years ago

      I found a formular for the sum, cos1+cos2+cos3.........+cosn. And also for sin, sinh, and cosh. I don't know, have this been found by mathematicians?

    • Pcunix profile image

      Tony Lawrence 7 years ago from SE MA

      Fifty years ago or more - I have no clue!

    • Manna in the wild profile image

      Manna in the wild 7 years ago from Australia

      Was it something like 'speed maths' or 'speed arithmetic'? something with 'speed' I think

    • Pcunix profile image

      Tony Lawrence 7 years ago from SE MA

      I learned this and many others from a book many, many years ago. I lost it and do not remember the title, unfortunately.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: ""

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)