Identification of Perfect Square Numbers

The purpose of this question is to determine which of the given numbers is not a perfect square. A perfect square is a number that is obtained by multiplying an integer by itself, that is, the square of an integer. For example, $9$ is a perfect square because $3^2 = 9$.

Main Characteristics of Perfect Square Numbers

It is useful to pay attention to the last digits of perfect square numbers for identification:

• The last digit of a perfect square number can only be 0, 1, 4, 5, 6, or 9.
• No perfect square number ever ends in 2, 3, 7, or 8.

Analysis of the Numbers

Let’s check the given options:

• 20163: The last digit of this number is 3. According to the property of perfect square numbers, any number ending in 3 cannot be a perfect square.
• 21316: The last digit of this number is 6. It could be a perfect square. $146 \times 146 = 21316$, so it is a perfect square.
• 10404: The last digit of this number is 4. It could be a perfect square. $102 \times 102 = 10404$, so it is a perfect square.
• 14641: The last digit of this number is 1. It could be a perfect square. $121 \times 121 = 14641$, so it is a perfect square.

Conclusion

Based on the above analysis, the number 20163 is not a perfect square because its last digit is 3, which is not a characteristic of a perfect square number.

Therefore, the correct answer is option A.