She asks for students to call out examples of

square numbers and the following exchange occurs:

For instance, we can already see that the

square numbers will appear on one diagonal of this 5-by-5 grid.

Explaining the relationship between the new number of stairs and the next

square number also proved to be difficult for the students, with several expressing confusion.

2] be a complete

square number, if there exists a positive integer m such that

According to Haylock and Manning (2014), connecting the geometric idea of a

square number as the number of items in a square array with the arithmetic idea that "a

square number is any number that is obtained by multiplying (a whole) number by itself" (p.

Smarandache asked us to study such a problem: How many perfect

square number are there in the sequence {a(n)I and {b(n)j?

The sum of the numbers assigned to the students in each pair must be a

square number.

The three business parks include: Property Submarket

Square Number of Footage Buildings Sorrento Tech I, II, III Sorrento Mesa 93,460 3 Pacific Point Sorrento Mesa 140,921 3 Centerpark Plaza I and II Miramar 200,398 9

This example illustrates that a link could be forged between the line number and the number of consecutive odd integers in each equation, as well as the

square number on the right side of the equation.

That is, a(n) is the smallest positive integer such that na(n) is a perfect

square number.

which is the relationship between succeessive triangular numbers and a

square number.

I have also seen students work together in small groups with calculators to discover if a thousand is a

square number and can be created through a grid pattern rather than individual pieces.