Here's how to find the square root of 1681 using the division method, step-by-step:
1. Grouping the Digits:
- Start by grouping the digits of the number (1681) in pairs, starting from the right. So, we have 16 and 81.
2. Finding the First Digit of the Square Root:
- Find the largest number whose square is less than or equal to the first group (16). In this case, it's 4 because 42 = 16.
- Write 4 as the first digit of the square root and also as the divisor.
- Subtract 16 (42) from the first group (16), which gives 0.
3. Bringing Down the Next Group:
- Bring down the next group of digits (81) next to the remainder (0). So, we have 081, which is just 81.
4. Finding the Next Digit of the Square Root:
- Double the quotient (4), which gives 8. Write 8 as the beginning of our new divisor, so we have 8. We need to find a digit to place in the blank such that (8)*(same digit) is less than or equal to 81.
- The digit is 1, because (81) 1 = 81. If we tried 2, we would get 82 2 = 164, which is too big.
- Write 1 as the next digit of the square root, and also write it after 8 in the divisor (81).
- Subtract 81 from 81, which gives 0.
5. Remainder Zero:
- Since the remainder is 0, the division is complete.
Therefore, the square root of 1681 is 41.
Summary in Tabular Form:
| Step | Action | Calculation | Result |
|---|---|---|---|
| 1 | Group digits | 16 81 | |
| 2 | Find first digit of square root | 4 * 4 = 16 | 4 is the first digit of the root |
| 3 | Subtract and bring down | 16 - 16 = 0, bring down 81 | 081 |
| 4 | Double quotient, find next digit | 4 2 = 8, 81 1 = 81 | 1 is the next digit of the root |
| 5 | Subtract and check for remainder | 81 - 81 = 0 | Remainder is 0, division complete. |
