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how to find square root of decimal number
To find the square root of numbers in the decimal form are explained in the following steps:
Step I: Make the number of decimal places even by affixing a zero on the extreme right of the decimal part (if required).
Step II: In the integral part, mark the periods as done while finding the square root of a perfect square of some natural number.
Step III: In the decimal part, mark the periods on every pair of digits beginning with the first decimal place.
Step IV: Now, find the square root by long division method.
Step V: Put the decimal point in the square root as soon as the integral part is exhausted.
Examples on square root of numbers in decimal form:
1. Evaluate: √42.25
Solution:
Using the division method we may find the square root of the given number;
Therefore, √42.25 = 6.5
2. Evaluate: √1.96
Solution:
Using the division method we may find the square root of the given number;
Therefore, √1.96 = 1.4
3. Evaluate: √6.4009
Solution:
Using the division method we may find the square root of the given number;
Therefore, √6.4009 = 2.53
4. Evaluate: √66.4225
Solution:
Using the division method we may find the square root of the given number;
Therefore, √66.4225 = 8.15
5. Evaluate: √0.4225
Solution:
Using the division method we may find the square root of the given number;
Therefore, √0.4225 = 0.65
square of a number easy trick math ssc bank po railway exam
square root
(algorithm)
Definition: This describes a “long hand” or manual method of calculating or extracting square roots. Calculation of a square root by hand is a little like long-hand division.
Suppose you need to find the square root of 66564. Set up a “division” with the number under the radical. Mark off pairs of digits, starting from the decimal point and working left. (Here the decimal point is a period (.) and commas (,) mark pairs of digits.)
___________
\/ 6,65,64.
Look at the leftmost digit(s) (6 in this case). What is the largest number whose square is less than or equal to it? It is 2, whose square is 4. Write 2 above, write the square below and subtract.
__2________
\/ 6,65,64.
-4
----
2
Now bring down the next two digits (65). The next “divisor” is double the number on top (2×2=4) and some other digit in the units position (4_).
__2________
\/ 6,65,64.
-4
-----
4_ ) 265
What is the largest number that we can put in the units and also multiply times the divisor such that the result is still be less than or equal to what we have? (Algebraically, what is d such that d × (40+d) ≤ 265?) It looks like 6 might work (since 6 × 40 = 240), but 6 is too big, since 6 × 46 = 276:
__2__6_____
\/ 6,65,64.
-4
-----
46 ) 265
-276 TOO BIG
So try 5 instead.
__2__5_____
\/ 6,65,64.
-4
-----
45 ) 265
-225
-------
40
Repeat: bring down the next two digits, and double the number on top (2 × 25 = 50) to make a “divisor”, with another unit.
__2__5_____
\/ 6,65,64.
-4
-----
45 ) 265
-225
-------
50_ ) 4064
It looks like 8 would work. Let’s see.
__2__5__8__
\/ 6,65,64.
-4
-----
45 ) 265
-225
-------
508 ) 4064
-4064
------
0
So the square root of 66564 is 258. You can continue for as many decimal places as you need: just bring down more pairs of zeros.
Here is an example spanning the decimal point. When a number does not have a rational square root, you can continue calculating (significant) digits as long as you wish.
__1__6.8_4_0_4_2_7_5_...
\/ 2,83.6
-1
-----
26 ) 183
-156
------
328 ) 2760
-2624
-------
3364 ) 13600
-13456
--------
33680 ) 14400
-0
---------
336804 ) 1440000
-1347216
----------
3368082 ) 9278400
-6736164
-----------
33680847 ) 254223600
-235765929
------------
336808545 ) 1845767100
-1684042725
-----------
161724375
Why does this work?
Consider (10A + B)² = 100A² + 2 × 10AB + B² and think about finding the area of a square. Remember that 10A + B is just the numeral with B in the units place and A in the higher position. For 42, A=4 and B=2, so 10 × 4 + 2 = 42.
The area of the two skinny rectangles is 2 × 10A × B. The tiny square is B². If we know A and the area of the square, S, what B should we choose?
We previously subtracted A² from S. To scale to 100A², we bring down two more digits (a factor of 100) of the size of S. We write down twice A (2A), but shifted one place to leave room for B (10 × 2A or 2 × 10A). Now we add B to get 2 × 10A + B. Multiplying by B gives us 2 × 10AB + B². When we subtract that from the remainder (remember we already subtracted A²), we have subtracted exactly (10A + B)². That is, we have improved our knowledge of the square root by one digit, B.
We take whatever remains, scale again by 100, by bringing down two more digits, and repeat the process.
See also cube root.
Note: In computers and hand-held calculators, square root, sine, cosine, and other transcendental functions are calculated with sophisticated functions, such as Taylor series, CORDIC, or Newton-Raphson method, sometimes called Newton’s method. This lesson explains, for instance, possible difficulties in convergence.
Author: PEB
Implementation
GAMS Class C2 has many implementations of powers, roots, and reciprocals (C and Fortran). Many variations (C and Assembler) for caching, pipelined processing, etc.
More information
Another geometric justification.
Go to the Dictionary of Algorithms and Data Structures home page.
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 8 September 2014.
HTML page formatted Mon Dec 12 09:26:39 2016.
Cite this as:
Paul E. Black, “square root”, in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 8 September 2014. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/squareRoot.html
How to find square of a number
and should your child learn how to do it
Most people in today’s world feel that since calculators can find square roots, that children don’t need to learn how to find square roots using any pencil-and-paper method. However, learning at least the “guess and check” method for finding the square root will actually help the students UNDERSTAND and remember the square root concept itself!
So even though your math book may totally dismiss the topic of finding square roots without a calculator, consider letting students learn and practice at least the “guess and check” method. Since it actually deals with the CONCEPT of square root, I would consider it as essential for students to learn.
Depending on the situation and the students, the “guess and check” method can either be performed with a simple calculator that doesn’t have a square root button or with paper & pencil calculations.
Finding square roots by guess & check method
To find a decimal approximation to, say √2, first make an initial guess, then square the guess, and depending how close you got, improve your guess. Since this method involves squaring the guess (multiplying the number times itself), it uses the actual definition of square root, and so can be very helpful in teaching the concept of square root.
Example: what is square root of 20?
You can start out by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5.
Then make a guess for √20; let’s say for example that it is 4.5. Square that, see if the result is over or under 20, and improve your guess based on that. Repeat this process until you have the desired accuracy (amount of decimals). It’s that simple and can be a nice experiment for students!
Example: Find √6 to 4 decimal places
Since 22 = 4 and 32 = 9, we know that √6 is between 2 and 3. Let’s guess (or estimate) that it is 2.5. Squaring that we get 2.52 = 6.25. That’s too high, so we reduce our estimate a little. Let’s try 2.4 next. To find the square root of 6 to four decimal places we need to repeat this process until we have five decimals, and then we will round the result.
| Estimate | Square of estimate | High/low |
| 2.4 | 5.76 | Too low |
| 2.45 | 6.0025 | Too high but real close |
| 2.449 | 5.997601 | Too low |
| 2.4495 | 6.00005025 | Too high so the square root of 6 must be between 2.449 and 2.4495. |
| 2.4493 | 5.99907049 | Too low |
| 2.4494 | 5.99956036 | Too low, so the square root of 6 must be between 2.4494 and 2.4495 |
| 2.44945 | 5.9998053025 | Too low, so the square root of 6 must be between 2.44945 and 2.4495. |
This is enough iterations since we know now that √6 would be rounded to 2.4495 (and not to 2.4494).
Finding square roots using an algorithm
There is also an algorithm for square roots that resembles the long division algorithm, and it was taught in schools in days before calculators. See the example below to learn it. While learning this algorithm may not be necessary in today’s world with calculators, working out some examples can be used as an exercise in basic operations for middle school students, and studying the logic behind it can be a good thinking exercise for high school students.
Example: Find √645 to one decimal place.
First group the numbers under the root in pairs from right to left, leaving either one or two digits on the left (6 in this case). For each pair of numbers you will get one digit in the square root.
To start, find a number whose square is less than or equal to the first pair or first number, and write it above the square root line (2):
| 2 | |
| √6 | .45 |
Then continue this way:
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| Square the 2, giving 4, write that underneath the 6, and subtract. Bring down the next pair of digits. | Then double the number above the square root symbol line (highlighted), and write it down in parenthesis with an empty line next to it as shown. | Next think what single-digit number something could go on the empty line so that forty-something times something would be less than or equal to 245. 45 x 5 = 225 46 x 6 = 276, so 5 works. |
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| Write 5 on top of line. Calculate 5 x 45, write that below 245, subtract, bring down the next pair of digits (in this case the decimal digits 00). | Then double the number above the line (25), and write the doubled number (50) in parenthesis with an empty line next to it as indicated: | Think what single digit number something could go on the empty line so that five hundred-something times something would be less than or equal to 2000. 503 x 3 = 1509 504 x 4 = 2016, so 3 works. |
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| Calculate 3 x 503, write that below 2000, subtract, bring down the next digits. | Then double the ‘number’ 253 which is above the line (ignoring the decimal point), and write the doubled number 506 in parenthesis with an empty line next to it as indicated: | 5068 x 8 = 40544 5069 x 9 = 45621, which is less than 49100, so 9 works. |
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Thus to one decimal place, √645 = 25.4
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Auto-Forward SMS and Missed Calls to your Email [Android]
you may wonder why would anyone want to forward text messages or missed call notifications to their email account when the cell phone is with them all the time? Won’t these messages add more noise to an overflowing email Inbox?
Not so. For instance, some of my friends work in a company where, for security reasons, they aren’t allowed to carry personal mobile phones inside though they do have regular phones at their desk and are allowed email access. They would therefore leave the phone at home but with auto-forwarding enabled, they’ll get an email alert as soon as someone sends them an SMS or calls on their cell during office hours.
Such a feature may also be handy for people who have recently switched to a different phone number and would like to keep track of all incoming calls and messages received on their previous phone but without having to carry it all the time.
The Android Market has dozens of apps that can bring the auto-forwarding feature to your mobile phone but the one that I like most is SMS2Gmail. It says “SMS” but the app can forward both SMS text messages and missed calls to your email address. You will get the complete message text in your email and the sender’s name as well provided that that number already exists in your phonebook.
sms auto forwardIt takes just one step to get it up and running. Launch the app, provide the credentials of your Gmail account and done. It needs the Google credentials in order to send email notifications but if that doesn’t make you too happy, just create another Gmail account and set it to auto-forward messages to your primary email account.
One more thing. You turn on email notifications manually but in a situation where you have have forgotten the phone at home, or have misplaced it somewhere, you can remotely activate auto-forwarding by sending an SMS from any another phone to your phone.
The app lets you assign an Activation Keyword (see screenshot) and as soon as a text arrives with that keyword, the auto-forwards will be enabled automatically.
Send SMS Text Messages from Computer to Mobile Phone via Outlook
With Microsoft Outlook 2007, you can easily send (or receive) SMS text messages from computer to any mobile phone – just write a new SMS text message (like the way you compose emails in Outlook) and hit Send.
Similarly, you can also forward emails, pending tasks and calendar items from Outlook to your mobile phone via SMS.
How to send SMS text messages from computer using Outlook 2007 ?
To SMS enable your copy of Microsoft Outlook 2007, first register your mobile phone number at SMSOfficer. This new service from Microsoft supports almost all cellular operators in US and other international countries including India.
You will soon get an SMS verification code on your mobile phone, confirm and the SMS feature is activated in your Outlook without you having to download any additional software – you will need to click on a configuration link which sets the entire configuration for you.
sms via email forwardForward Emails as SMS Text Messages
To compose an SMS message in Outlook, select New -> Text Message. Outlook is automatically set up to use the standard text message limit of 160 characters. If your message exceeds the 160 character limit, the extra characters are truncated and delivered as a separate text message.
There are no registration charges and you also get 10 SMS credits for free at the time of joining SMS Officer. Once you exhaust the free limit, you need to pay for using the Outlook SMS service – payment can be made via PayPal.
When the other person replies to your SMS message, it will arrive in your mobile phone. Am not sure if you can use Outlook 2007 to send bulk SMS messages – i.e., one SMS message addressed to multiple recipeints.
How to Get SMS Alerts for Gmail via Twitter
You can use Twitter as a Gmail notifier and receive SMS text alerts on your mobile phone for new email messages in your GMail mailbox.
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Twitter SMS Arrives in India via Airtel
Auto-Forward SMS and Missed Calls to your Email [Android]
Twitter Guide: How To Do Interesting Things With Twitter
Post to Twitter from Mobile Phones Without SMS
How to Monitor your Website’s Uptime with Google Docs
How do you get SMS notifications on your mobile phone for important emails in your Gmail? Google doesn’t support text notifications for their email service but Twitter does. If we can figure out a way to connect our Twitter and Gmail accounts, the Gmail notifications can arrive as text on our mobile via Twitter. Let me explain:
Twitter allows you to follow any @user via a simple SMS. They provide short codes for all countries (see list) and if you text FOLLOW to this shortcode following by the username, any tweets from that user will arrive in your phone as text notifications. For instance, if you are in the US, you can tweet FOLLOW labnol to 40404 to get my tweets as text messages. Similarly, users in India can text FOLLOW labnol to 9248948837 to get the tweets via SMS.
The short code service of Twitter can act as a Gmail SMS notifier. You create a new Twitter account, set the privacy to private and this account will send a tweet when you get a new email in Gmail. Follow this account via SMS from you main Twitter account and the SMS notifications will start pouring in.
<img src=”http://img.labnol.org/di/gmail_twitter.png” height=”555″ width=”555″></img><br>
Use Twitter as a Gmail Notifier with Google Scripts
Here’s a step by step guide on how you can use Twitter to get SMS notification for important email in your Gmail account. It will take a minute to setup and, internally, there’s a Google Apps Script that’s doing all the magic. It monitors your Gmail mailbox in the background and as soon as a new message arrives in your account, the script sends out a tweet.
- Log out of your existing Twitter account and then go to twitter.com/signup to create a new Twitter account for your Gmail account.
- Confirm your email address, then open the Twitter settings page and check the option “Protect My Tweets.” This will make your Gmail notifications private and neither search engines nor other Twitter users will be able to see tweets generated through Gmail.
- Click here to copy the Google Sheet and choose Authorize under the Gmail to Twitter menu (near Help). Remember to authorize with your new Twitter account.
- Once authorized, choose Start from the Gmail to Twitter menu and enter yourGmail search query. For instance you can say is:important is:unread in:inbox newer_than:1d to only receive notification for new, unread and important emails in your Gmail. Click OK.
That’s it. The Gmail notifier is running and it will tweet when a matching email is found. It runs every 10-15 minutes and will only work on incoming email, not the old message. The messages will also be logged in the Google Sheet so you know what’s happening behind the scene.
Get SMS Alerts for Emails at Gmail
Open a new browser session in Incognito mode, log in to your old Twitter account and send a follow request to your new Gmail account on Twitter. Approve the new follower request and you should now see tweets for new Gmail messages, as they arrive, in your main Twitter timeline.
Should you wish to receive SMS alerts on your mobile phone for new Gmail messages, just open the Twitter profile page of your Gmail bot and turn on Mobile Notifications. This will obviously work only if you have connected (and verified) your mobile phone with your main Twitter account.
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play with google
1. Google Gravity
Watch Google shattering itself under the effect of gravity. But the funny part is, you can still make a search by entering your query in the search box and it will display the results in gravity fashion.
2. Google Mirror
Watch google creating the mirror image every you type with google mirror.
To do this :
Open google.com and type in google mirror and select I’m feeling lucky or the first link that comes up.
eramarswami.com 
