The number of zeroes at the end of the square of a number is _______ the number of zeroes at the end of the number

Answer

To solve the question, "The number of zeroes at the end of the square of a number is _______ the number of zeroes at the end of the number," we will analyze the relationship between the number of zeroes at the end of a number and its square.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to determine how the number of zeroes at the end of a number relates to the number of zeroes at the end of its square.

2. **Identifying the Number of Zeroes**:
Let's take a number that ends with a certain number of zeroes. For example, consider the number 10, which has 1 zero at the end.

3. **Calculating the Square**:
Now, we will square the number:
\[ 10^2 = 100 \]
The result, 100, has 2 zeroes at the end.

4. **Generalizing the Example**:
Let's take another example, the number 20:
\[ 20^2 = 400 \]
Here, 20 has 1 zero at the end, and 400 has 2 zeroes at the end.

5. **Further Example**:
Consider the number 100:
\[ 100^2 = 10000 \]
The number 100 has 2 zeroes at the end, and 10000 has 4 zeroes at the end.

6. **Conclusion**:
From the examples above, we can see that the number of zeroes at the end of the square of a number is always double the number of zeroes at the end of the original number. Therefore, we can fill in the blank in the question:
\[ \text{The number of zeroes at the end of the square of a number is } \textbf{twice} \text{ the number of zeroes at the end of the number.} \]