Solution:

To find the number of digits in the square root of 25600, we need to first calculate the square root of 25600.

Finding the Square Root of 25600:

We can use the long division method to find the square root of 25600 as follows:

1. Starting from the right, we pair the digits of 25600 by placing a bar above them. If there is an odd number of digits, the leftmost digit is paired with a zero.

2. We find the largest square number that is less than or equal to the first paired digits (25 in this case). The square of 5 is 25, so we write 5 as the first digit of the square root.

3. We subtract the product of the square root digit and itself (i.e., 5 x 5 = 25) from the first paired digits (25), and bring down the next pair of digits (600) next to the remainder.

4. We double the first digit of the current partial remainder (i.e., 5 x 2 = 10), and find the largest digit that, when multiplied by itself and added to this product, gives a result less than or equal to the current partial remainder (i.e., 10 || 0). The largest digit is 2, since 22 x 2 + 0 = 88 which is less than 100.

5. We write the digit 2 as the second digit of the square root, and write 22 below the current partial remainder. We subtract the product of the current square root digit and the two digits below it (i.e., 52 x 2 = 100) from the current partial remainder (i.e., 100), and bring down the next pair of digits (00) next to the remainder.

6. We repeat steps 4 and 5 until we get the desired level of accuracy.

The completed long division process is as follows:

5
_______
√25600
25
_____
600
500
_____
1000
1000
_____
0

Therefore, the square root of 25600 is 160.

Finding the Number of Digits in the Square Root:

To find the number of digits in the square root of 25600, we simply count the number of digits in 160, which is 3. Hence, the correct option is (a) 3.