Approximating Square Roots
Approximating Square Roots
To find the approximate square root of a number, we shall use the method of long division. Using this method we shall obtain square root correct to certain decimal places. The steps are as followed
Step I: Obtain the number whose square root is to be computed.
Step II: Determine the number of decimal places to which the square root of the number is to be computed.
Suppose the square root of the given number is to be computed correct to n places of decimal.
Step III: Count the number of digits in the decimal part. If the number of digits is less than 2n, then affix a suitable number of zeroes at the extreme right of the decimal part so that the number of digits in the decimal part becomes 2n.
Step IV: Use the method of long division to find the square up to (n+1) places of decimal.
Step V: Check the digit at (n+1)th decimal place, if it is less than 5, then delete it to get the answer correct to n decimal places.If the digit at (n+1)th decimal place is 5 or more than, then increase the digit at nth decimal place by one and delete the digit at 9n+1)th place to obtain the square root correct up to n decimal places.
Illustration: Find the square root of 2 correct to three places of decimal.
Solution: Since we have to find the square root of 2 correct to three places of decimal,we shall first find the square root of 2 up to four places of decimal.for this purpose,we affix 8 zeros to the right of the decimal point.o we write
2 = 2.00000000
Now mark off periods and proceed as under:
up to four places of decimal.
, correct up to three places of decimal.
Hence
Approximate values of Square Roots Using Square Root Tables
In many practical problems, we need the square roots of numbers, and finding approximate values of square roots of numbers by the method of long division is very time-consuming.for this reason, tables have been prepared which provide the approximate values of square roots of different numbers correct to a certain decimal place.
The following table gives values of square roots of all-natural numbers 1 to 24.
| x | x | x | x | ||||
| 1 | 1.000 | 7 | 2.646 | 13 | 3.606 | 19 | 4.359 |
| 2 | 1.414 | 8 | 2.828 | 14 | 3.742 | 20 | 4.472 |
| 3 | 1.732 | 9 | 3.000 | 15 | 3.873 | 21 | 4.583 |
| 4 | 2.000 | 10 | 3.162 | 16 | 4.000 | 22 | 4.690 |
| 5 | 2.236 | 11 | 3.317 | 17 | 4.123 | 23 | 4.796 |
| 6 | 2.449 | 12 | 3.464 | 18 | 4.243 | 24 | 4.899 |
Illustration: By using the table for square roots, find the value of .
What is the divisor in the third step while finding the square root of 66. | |||
| Right Option : B | |||
| View Explanation | |||
What is the divisor in the second step while finding the square root of 2 using the approximation method. | |||
| Right Option : B | |||
| View Explanation | |||
By using the table for square roots, find the value of | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
Aman Kumar Shrivastava
10thUsually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...
Anika Saxena
8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...
Shreya Shrivastava
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thAbout Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
Shreya Shrivastava
8thWe started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.
Manya
8thAbhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.
Barkha Arora
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
Ayan Ghosh
8thAbhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of performance in Abhyas exams. He is satisfied with institute.
Yogansh Nyasi
7thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thAbhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary because of Abhyas.Teacher have very friendly atmosphere also.
Manish Kumar
10thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thMy experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills developed and now I am the first one to give the answer of teachers question.
Upmanyu Sharma
7thThe experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
10thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
Aman Kumar Shrivastava
10thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thMy experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should join Abhyas Academy in tenth class as I am seeing much improvement in Maths and English
Hridey Preet
9thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
