A perfect square is an integer that can be expressed as the square of another integer. In other words, if an integer $n$ is a perfect square, then there exists some integer $k$ such that:

$n = k^2$

For example:

• $1 = 1^2$
• $4 = 2^2$
• $9 = 3^2$
• $16 = 4^2$
• $25 = 5^2$

Thus, the numbers 1, 4, 9, 16, 25, and so on are all perfect squares because they are squares of whole numbers.

Perfect squares have some interesting properties:

• They always have an odd number of total divisors.
• The square root of a perfect square is always an integer.

Would you like more examples of perfect squares or to explore more properties?

Here are 5 questions that relate to perfect squares:

1. Can the sum of two perfect squares also be a perfect square?
2. What are the properties of the differences between consecutive perfect squares?
3. How do perfect squares behave in modular arithmetic?
4. Is there a way to quickly recognize if a number is a perfect square?
5. What are the applications of perfect squares in geometry?

Tip: When dealing with perfect squares, remember that they grow quadratically, meaning their size increases rapidly as the base number increases.