Define perfect squares geometrically and algebraically, and identify rules for their unit digits and trailing zeroes.
Resolving the locker puzzle using factor pairs and introducing squares.
Why do only certain lockers remain open? In the puzzle, a locker changes state (open to closed, or closed to open) every time a person touches it. If it is touched an odd number of times, it will stay open at the end.
Shows the geometric origin of the term 'square' using grids of varying unit areas.
The number of unit squares inside a square corresponds to the product of its sides.
Formal definition and notation for squares.
Rules for identifying numbers that cannot be squares.
Can you tell if a number is a perfect square just by looking at its last digit? Yes, but mostly to rule numbers out! Perfect squares always end with the digits 0, 1, 4, 5, 6, or 9.
Identify which numbers cannot be perfect squares by inspection.
Which of the following numbers could potentially be a perfect square based purely on its unit digit?
Practice squaring a fractional and decimal base.
To compute the square of a fraction or a decimal, we multiply the number by itself. For example, the text shows that the square of is calculated as . We can use this same process to find the square of . By multiplying the numerator and the denominator by themselves, we get . Similarly, we can calculate the squares of decimals like . Following this pattern to find the square of , we expand the expression as . When we multiply these decimal values, we find that the final squared result is .