Before we dive into finding square and cube numbers between 10 and 90, let’s understand the basics of these concepts.
Square Numbers
A square number is the result of multiplying a whole number by itself. In other words, it’s the product of a number and its own value.
Here are some examples of square numbers:
- 1 x 1 = 1 (1 is a square number)
- 2 x 2 = 4 (4 is a square number)
- 3 x 3 = 9 (9 is a square number)
- 4 x 4 = 16 (16 is a square number)
- 5 x 5 = 25 (25 is a square number)
You can represent square numbers visually as squares. For example, the square number 9 can be represented as a square with 3 rows and 3 columns of dots:
TextCopy* * *
* * *
* * *
Cube Numbers
A cube number is the result of multiplying a whole number by itself three times. It’s the product of a number multiplied by itself, and then multiplied by itself again.
Here are some examples of cube numbers:
- 1 x 1 x 1 = 1 (1 is a cube number)
- 2 x 2 x 2 = 8 (8 is a cube number)
- 3 x 3 x 3 = 27 (27 is a cube number)
- 4 x 4 x 4 = 64 (64 is a cube number)
- 5 x 5 x 5 = 125 (125 is a cube number)
You can visualize cube numbers as three-dimensional cubes. For instance, the cube number 8 can be represented as a cube with 2 rows, 2 columns, and 2 layers of dots.
Finding Square and Cube Numbers Between 10 and 90
Now, let’s find the square and cube numbers that fall between 10 and 90.
Square Numbers
We need to find the square numbers that are greater than 10 and less than 90. Let’s start by listing out the squares of consecutive whole numbers:
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81
- 10² = 100
From this list, we can identify the square numbers between 10 and 90: 16, 25, 36, 49, 64, and 81.
Cube Numbers
Similarly, let’s list out the cubes of consecutive whole numbers:
- 1³ = 1
- 2³ = 8
- 3³ = 27
- 4³ = 64
- 5³ = 125
The cube numbers between 10 and 90 are 27 and 64.
Summary
Therefore, the square numbers between 10 and 90 are: 16, 25, 36, 49, 64, and 81. The cube numbers between 10 and 90 are: 27 and 64.
Key Takeaways
- Square numbers are the result of multiplying a number by itself.
- Cube numbers are the result of multiplying a number by itself three times.
- To find square and cube numbers within a range, you can list out the squares and cubes of consecutive whole numbers and identify those that fall within the desired range.