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 .
Find the divisor in the fourth step while finding the square root of 2 using the approximation method. | |||
| Right Option : A | |||
| View Explanation | |||
What is the divisor in the third step while finding the square root of 0.4285714285.
| |||
| Right Option : A | |||
| View Explanation | |||
By using the table for square roots, find the value of | |||
| Right Option : B | |||
| View Explanation | |||
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