Square Numbers

Hello mathematicians, puzzlers, and other curious people!

For those who don\’t already know, when you take a number and multiply it by itself, the product is called a square number because we can use it to draw a square neatly, such as these numbers:

Sometimes you will hear people refer to numbers as \”___ squared,\” especially as a step in a problem. For example, 16 is the same as \”four squared.\”

You might also hear the number multiplied by itself referred to as the square root of the product. For example, 3 is the square root of 9.

Square numbers can be interesting to investigate. More questions than these are definitely possible, but here\’s a list of questions to start you off:

• What happens when you add square numbers? Subtract them? Multiply them? Divide them?
• What patterns can you find in the sequence of square numbers? (1, 4, 9, 16, …)
• What different groups can you organize square numbers into?
• Can you find efficient ways to tell if a number is square or non-square?
• How can you calculate a square number\’s square root?
• Can fractions be square numbers?

I\’ll post some investigations based on these and other questions about square numbers, but don\’t let that slow you down — instead, see what you can figure out.

Calc You Later!

Update: This post has a sequel in which I investigate the results of multiplying square numbers.