how to find square root by division method
Answers
2. Pair digits together to the left of the decimal. Again pair digits to the right of the decimal. Perhaps there is only one digit unpaired on the leftmost. Add a zero on the rightmost (of fraction if needed to make a pair).
3. Draw a line above the number. Draw a vertical line to the left of the number.
4. Take the leftmost pair (or unpaired digit) with value n. Find x such that x² <= n. Write x on the top of the number. Write x to the left of the margin.
5. Write x² below the number. Subtract it to get remainder R.
6. Bring down the next pair of digits next to R. So we get number n now.
7. Write down 2*x (call it y) on the left margin to the left of this n.
8. We need to find a new digit x such that (10*y+x) *x <= n. Write that. Write this new x on the top of the given number.
9. Write (10 y+x)* x below n and subtract it.
10. Now import the next pair of digits and continue the above steps.
11. If the decimal place is encountered, then write a decimal on the quotient above the horizontal line (above the given number).
12. Continue with the fraction too, till the required accuracy.
Example:
2 .
9 6 x quotient = answer
==========
| 8 . 82 given number
2 | 4
find x such that x * x <= 8, so x = 2
| =======
subtract 4 from 8 and write two times 2, on left side
| 4 82
import 82 from top. put a decimal point in the 1st
line (top).
49 | 4 41
find x such that x * (4x) <= 482. so 9 *
49 < 482
| ======
| 41 00
write 2 times 29 (from top line) as 58 on the left.
586 | 35 16 find 6 such
that 6 * 586 < 4100
========
592x | 5 84 00 continue like
that. find x now.
Explanation:
To find the square by long division method we follow the following steps:
(i) First we make the pair of the digits starting from the digit's at one's place.
For making the pair place a bar over every pair of digits.
If the number of digits in it odd, then the left-most single digit will have a bar.
(ii) Find the largest number whose square is less than or equal to the number under the extreme left bar.
Take this number as the divisor and the number under the extreme left bar as dividend.
Divide and get the remainder.
(iii) To the right of the remainder place the number that is under the next bar.
(iv) Now double the divisor and enter it with blank on its right.
(v) Think a largest possible digit to fill the blank which will also become the new digit in the quotient such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend.
(vi) Repeat these steps till get the remainder 0 and no digits are left in the given number.
Example:
Find the square root of 529 by long division method.