Square Root Using Long Division
Square Root Using Long Division
When the square numbers are very large, the method of finding their square roots by prime factorization becomes very lengthy and difficult also. In such cases, we use the method of long division to find the square root. We follow the following step wise procedure to find the square root of squares by the long division method.
Procedure:
STEP I Obtain the number whose square root is to be computed.
STEP II Place bars over every pair of digits starting with the units digit. Also, place a bar on one digit (if any) not forming a pair on the extreme left. Each pair and the remaining one digit (if any) on the extreme left is called a period.
STEP III Think of the largest number whose square is less than or equal to the first period. Take this number as the divisor and the quotient.
STEP IV Put the quotient above the period and write the product of divisor and quotient just below the first period.
STEP V SUbtract the product of divisor and quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.
STEP VI Double the quotient as it appears and enters it with a blank on the right for the next digit, as the next possible divisor.
STEP VII Think of a digit, to fill the blank in step VI, in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend obtained in step V.
STEP VIII Subtract the product of the digit chosen in step VII and the new divisor from the dividend obtained in step V and bring down the next period to the right of the remainder. This becomes a new dividend.
STEP IX Repeat steps, VI, VII, and VIII till all periods have been taken up.
STEP X Obtain the quotient as the square root of the given number.
The following illustration will illustrate the above procedure.
Illustration: Find the square root of 4937284 by the long division method.
(i) 4937284
SOLUTION
What is the first period while calculating the square root of 7569 using the method of long division. | |||
| Right Option : C | |||
| View Explanation | |||
Find the last divisor while calculating the square root of 54756 using the long division method. | |||
| Right Option : B | |||
| View Explanation | |||
What is the first period while calculating the square root of 12544 using the method of long division. | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
My 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
10thMy 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
8thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
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
7thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thWhen I have not joined Abhyas Academy, my skills of solving maths problems were not clear. But, after joining it, my skills have been developed and my concepts of science and SST are very well. I also came to know about other subjects such as vedic maths and reasoning.
Sharandeep Singh
7thAbhyas 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
7thAbhyas 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
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
9thUsually 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
8thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
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
8thMy 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
8thIt 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
Barkha Arora
10thAbhyas 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
10thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thThird 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
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
10thAbhyas 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.
