1. The problem asks: What is a perfect square? 2. A perfect square is a number that can be expressed as the square of an integer. 3. The formula for a perfect square is: $$n = k^2$$ where $k$ is an integer. 4. Important rules: - The square of any integer (positive, negative, or zero) is a perfect square. - Examples: $1 = 1^2$, $4 = 2^2$, $9 = 3^2$, $16 = 4^2$, etc. 5. To check if a number is a perfect square, find its square root and see if the result is an integer. 6. For example, to check if $25$ is a perfect square: $$\sqrt{25} = 5$$ Since $5$ is an integer, $25$ is a perfect square. 7. To check if $20$ is a perfect square: $$\sqrt{20} \approx 4.472$$ Since $4.472$ is not an integer, $20$ is not a perfect square. Final answer: A perfect square is any number that can be written as $k^2$ where $k$ is an integer.