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
Find the divisor at the second stage in the square root of 784 while calculating its square root using the method of long division. | |||
| Right Option : A | |||
| 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 is the first period while calculating the square root of 7569 using the method of long division. | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [10]
Abhyas 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
10thOne 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
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 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
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
7thBeing 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
8thIt 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
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
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.
