find the square root of 136 161 by using division method
The correct answer and explanation is:
To find the square root of 136161 using the division method, follow these steps:
- Group the Digits: Begin by pairing the digits of the number from right to left. For 136161, we group it as (13)(61)(61).
- Find the Largest Square Less Than or Equal to the First Group: Look at the first group, which is 13. The square of 3 is 9, which is the largest square less than or equal to 13. So, write 3 as the first digit of the square root. Subtract 9 from 13 to get 4. Bring down the next pair, which is 61, making the new dividend 461.
- Double the Current Root and Use It as the Divisor: Double the current root (3), giving 6. Now, find a number that, when added to 6 and multiplied by the new number, gives a product close to 461. Try 7: (6+7) × 7 = 91. Since 91 is less than 461, it works. Write 7 as the next digit of the square root.
- Subtract and Bring Down the Next Pair: Subtract 91 from 461 to get 370. Now, bring down the next pair, which is 61, making the new dividend 37061.
- Repeat the Process: Double the current root (37), giving 74. Try 5: (74+5) × 5 = 395. Since 395 is less than 37061, try 6. (74+6) × 6 = 480, which is still less than 37061.
By repeating this method, you would get a root of approximately 369.
Explanation:
The division method involves progressively finding digits of the square root by testing numbers and refining the estimate based on subtraction and division steps. The process helps ensure accuracy by narrowing down possible values for each digit, working from left to right.