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
A general arranges his soldiers in rows to form a perfect square . He finds that in doing so,60 soldiers are left out.if the total number of soldiers be 8160, find the number of soldiers in each row. | |||
| Right Option : B | |||
| View Explanation | |||
Find the divisor at the second stage in the square root of 676 while calculating its square root using the method of long division. | |||
| Right Option : A | |||
| View Explanation | |||
What will be the number of digits in the square root of 25600 ? | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [20]
One 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
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
8thMy 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
8thAbout 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
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
10thA 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
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
8thWhen 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
7thIt 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
10thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thIt 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 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
10thIt 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
10thThe 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 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
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
8thIn 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
10thAbhyas 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 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.
