Perfect Squares and Their Patterns
Why square numbers are called squares.
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The number of unit squares inside a square corresponds to the product of its sides.
What makes a number a perfect square, and the digit patterns that give non-squares away.
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Why only the perfect-square lockers stay open.
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.
Why square numbers are called squares.
The number of unit squares inside a square corresponds to the product of its sides.
What a square number is, and how to write it.
Last digits and zeros that tell you a number can't be a square.
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.
Spot the numbers that can't be perfect squares.
Which of the following numbers could potentially be a perfect square based purely on its unit digit?
Square fractions and decimals.
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 .