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 .
By using the table for square roots, find the value of | |||
| Right Option : D | |||
| View Explanation | |||
What is the divisor in the third step while finding the square root of 66. | |||
| Right Option : B | |||
| View Explanation | |||
By using the table for square roots, find the value of | |||
| Right Option : B | |||
| 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
10thBeing 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
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
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
7thI 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
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
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
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
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
