Answer:
√576 = 24
Explanation:
You want to find the square root of 576 by the long division method.
Method
The attachment shows the result of applying the method.
- The dividend is marked off in 2-digit groups working outward from the decimal point. An overline is typically used. Here, 76 is the group closest to the decimal point, and the next "group" is 5
- The integer part of the square root of the leftmost 2-digit group is written as the leftmost digit of the root. Here the integer part of the square root of 5 is 2, so that is the first root digit.
- The quotient digit is appended to the divisor, and the result is multiplied by the root digit. For the first step here, the digit 2 is appended to 0, and multiplied by the root digit 2. The product, 4, is subtracted from the dividend so far, and the next 2-digit group is appended to the result to form the next "dividend."
- The root so far is doubled and written as the first digits of the new divisor. This will be 2·2 = 4, with space left to append the next root digit: 4_.
- The next root digit is the largest integer that can be appended to the divisor, and multiplied by that divisor to obtain a value that is at most equal to the "dividend." Here, the second digit of the root is 4, and 44 · 4 = 176. This value is subtracted from the dividend resulting from step 3. Here, they are equal, so the difference is zero, and we're done.
- If there are more digits and/or the difference is not zero, then the process is repeated from step 3.
The root of 576 is 24.