How can we find the square root of 6400 by division method??
The correct answer and explanation is:
To find the square root of 6400 using the long division method, follow these steps:
- Group the Digits: Start by grouping the digits of 6400 in pairs, beginning from the right. So, 6400 is grouped as 64 and 00.
- Find the Largest Square Less Than 64: Find the square of numbers starting from 1. The square of 8 is 64, which is the largest square less than or equal to 64. So, 8 is the first digit of the square root.
- Subtract the Square: Subtract the square of 8 (which is 64) from 64: 64−64=064 – 64 = 0 Now, bring down the next pair, which is 00, making the number 00.
- Double the Divisor: The divisor now is 8, so double it to get 16. Write 16 and leave a space for the next digit.
- Divide: Now, place a digit in the space. Find a number such that when you multiply it by the new divisor (16 with the new digit), the product is less than or equal to the number you have after bringing down the next pair (00). Here, the digit is 0 because 160 multiplied by 0 is 0, and we have no value to subtract.
- Continue: There are no more pairs to bring down, and the remainder is 0. Therefore, the square root of 6400 is 80.
Explanation:
The long division method is a step-by-step process for finding square roots manually. It involves grouping digits in pairs, dividing, and subtracting in stages. This method works by estimating the square root through successive approximations. Each step reduces the problem to smaller numbers, eventually giving the correct result.
In the case of 6400, the method reveals that the square root is 80. By doubling the divisor and bringing down the pairs of digits, we can systematically narrow down the correct root without guessing.