Square Root Formula

Jump to Last Post 1-6 of 6 discussions (10 posts)
  1. profile image50
    mosesb44posted 14 years ago

    Does anyone have a formula for finding the square root of a number? I know that one can use a calculator but there is a formula in the calculator in order for it to perform. I would like to have the formula along with an example.

    Thank you.
    Bernard Moses

    1. profile image0
      EmpressFelicityposted 14 years agoin reply to this

      Try the second of the two methods shown in this:

      http://www.homeschoolmath.net/teaching/ … orithm.php

      I must say the first method (the "guess and check" one) looks a lot easier!

    2. fatfist profile image78
      fatfistposted 14 years agoin reply to this




      Calculators have built-in routines which compute exponential functions and natural logarithms. With these tools in place they can quickly compute a multitude of goodies, such as the square root. A calculator does it as follows:

      sqrt(X) = e (0.5 * ln (X))

      where e = exponential func, and ln = natural log

      That's how a slide rule does it as well.


      But, there are hundreds of successive approximating algorithms that you can use to write your own programming routine to calculate square roots from scratch.

    3. Reenile profile image60
      Reenileposted 14 years agoin reply to this

      Hey Bernard,
        I just posted a hub about a quicker way of finding the square root. See it here http://hubpages.com/hub/Shortcut-Method … uare-Roots

  2. HABMATH profile image80
    HABMATHposted 14 years ago

    As far as I can recall the formula is obtained through calculus. I believe it is called Newton's Method for approximating roots of equations. (any root can be obtained.)
    Or perhaps a Taylor Series is used.
    When I was in High School (precalculator days) we learnt a method for computing square roots. This method can be found in older high school math books.
    An interesting (and simpler method though a calculator is helpful for this) is to obtain the square root through successive approximations.
    For instance you need to find the square root of 6.
    6 lies between 4 and 9.Therefore the square root lies between 2 and 3. calculate (2.5)^2 This is 6.25 a tad too big. Now try (2.25)^2 Continue by changing the decimal value until you obtain the accuracy you need.

  3. kirstenblog profile image77
    kirstenblogposted 14 years ago

    I asked my high school math teacher this and he couldn't answer! Crazy!

  4. Ben Evans profile image74
    Ben Evansposted 14 years ago

    It would be hard for us to calculate square roots the same way that a calculator would.  The use an approach based on logarithms.

    Math can be expressed mechanically by a cam or electronically through a circuit or by an algorithm like a computer or calculator. 

    Most estimation methods are iterative:

    Lets look at a way to find square roots:

    Well lets memorize five for now

    2^1/2=1.41
    3^1/2=1.73
    5^1/2=2.24
    7^1/2=2.65
    11^1/2=3.32

    If you notice, I picked only prime numbers because all other numbers are combination of the primes.  Now normally, I would memorize 20.  I used to do this and would very quickly calculate square roots. 

    Lets start here:  Okay we don't have 6.  6^1/2sad2^1/2)(3^1/2)=2.44

    Now you can see why I just use primes:

    Now lets say we want to find 80^1/2.  This is (16^1/2)(5^1/2)=4(2.24)=8.96

    Try your calculator and it will come incredibly close.

    So lets say we want to find the square root of 331.

    Pretty tricky right?

    331 is close to 330 okay
    and 330 is 2*5*3*11

    and 330^1/2sad2^1/2)(5^1/2)(3^1/2)(11^1/2)=1.41*2.24*1.73*3.32=18.14

    331^1/2=18.19

    You can actually iterate at this point and you will be very close.

    If you have 20 primes memorized, you can calculate very large numbers fast and accurately.

    I hope this helps.

    1. Ben Evans profile image74
      Ben Evansposted 14 years agoin reply to this

      I have to seperate the equals form the paranthesis because it gives a sad face.  big_smile

      330^1/2= (2^1/2)(5^1/2)(3^1/2)(11^1/2)=1.41*2.24*1.73*3.32=18.14

      6^1/2= (2^1/2)(3^1/2)=2.44

  5. profile image0
    Deborah Sextonposted 14 years ago
  6. sorana profile image59
    soranaposted 14 years ago

    Well, there is a way of calculating a square root by hand. Seeing how many people were having trouble with this I've just written a hub on 'Square Root of a Number by Hand'. And yes, it can be done by hand, calculators were programmed by people who knew the algorithm. Have fun ... always ... with Maths!

 
working

This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com 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: https://corp.maven.io/privacy-policy

Show Details
Necessary
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 googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
Features
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)
Marketing
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.
Statistics
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)
ClickscoThis is a data management platform studying reader behavior (Privacy Policy)