1. What are Square Numbers?

A square number (or a perfect square) is a number that results from multiplying an integer by itself.

For example:

• $1\times 1=1$ → 1 is a square number
• $2\times 2=4$ → 4 is a square number
• $3\times 3=9$ → 9 is a square number
• $4\times 4=16$ → 16 is a square number

Thus, the sequence of square numbers is:
$1,4,9,16,25,36,49,64,81,100,\dots$

2. What is a Perfect Square?

A perfect square is any number that can be expressed as the square of a whole number.

For example:

• $25=5\times 5$, so 25 is a perfect square.
• $49=7\times 7$, so 49 is a perfect square.
• $00=10\times 10$, so 100 is a perfect square