Square numbers are formed by multiplying a number by itself. What is the square of 5?

25, since 5 × 5 = 25.

A number is a square number if it has a factor pair where both factors are equal. True or False?

True.

Fill in the blank: The number 36 is a square number because it can be expressed as ___ × ___.

6 × 6.

Which of the following is a square number: 10, 15, 16, or 20?

16, because it equals 4 × 4.

Riddle: I am a number that is the result of multiplying 4 by itself, what number am I?

16.

What is the visual representation of the square number 9?

It can be represented as a 3 × 3 grid of squares.

Adding consecutive odd numbers produces square numbers. What is the result of adding the first four consecutive odd numbers?

16, because 1 + 3 + 5 + 7 = 16 which is 4².

Square numbers can be represented as squares made of smaller squares. What is the square representation of 1?

It is represented by 1 × 1, which is 1 square.

Factor pairs identify square numbers. What are the factor pairs of 25, and why is it a square number?

The factor pairs of 25 are (1, 25) and (5, 5); it is a square number because 5 × 5 = 25.

Triangular numbers can be represented visually as ___ arrangements.

Triangular arrangements of dots or objects.

True or False: The number 36 is both a square and a triangular number.

True. 36 is 6² (square) and can be expressed as 1 + 2 + 3 + 4 + 5 + 6 (triangular).

Fill in the blank: The first five triangular numbers are ___ .

1, 3, 6, 10, 15.

Example of a number that is both square and triangular is ___ .

1, since 1 = 1² (square) and also 1 (triangular).

What happens when you add pairs of triangular numbers?

Adding pairs of triangular numbers can produce square numbers, for example, 1 + 3 = 4 = 2².

Riddle: I am a number that can be arranged in a triangle and also a square. What number am I?

36, as it can be arranged as both a square (6²) and a triangular number (1 + 2 + 3 + 4 + 5 + 6).

A number is divisible by 2 if its ___ digit is even.

Ones

True or False: A number is divisible by 4 if the last two digits form a number that is divisible by 4.

True

Fill in the blank: A number is divisible by 8 if the last ___ digits form a number divisible by 8.

Three

What is the condition for a number to be divisible by 4?

The last two digits of the number must form a number that is divisible by 4.

Riddle: I am a number; check my last three digits to see if I am divisible by eight. What am I?

A number that is divisible by 8.

True or False: Every hundred is divisible by 2.

True

What example demonstrates that 1,736 is divisible by 2?

The ones digit is 6, which is even.

Fill in the blank: Since 100 = 4 x 25, every ___ is divisible by 4.

Hundred

Short Answer: Explain how to determine if a number is divisible by 8.

Check if the last three digits of the number form a number that is divisible by 8.