Let’s investigate perfect squares and perfect cubes.
The number 9 is a perfect square.
Find four numbers that are perfect squares and two numbers that are not perfect squares.
Use the 32 snap cubes in the applet’s hidden stack to build the largest single cube you can. Each small cube has side length of 1 unit.
This applet has a total of 64 snap cubes. Build the largest single cube you can.
The number 27 is a perfect cube.
Find four other numbers that are perfect cubes and two numbers that are not perfect cubes.
Make sure to include correct units of measure as part of each answer.
When we multiply two of the same numbers together, such as $5\boldcdot 5$, we say we are squaring the number. We can write it like this: $$5^2$$Because $5\boldcdot 5 = 25$, we write $5^2 = 25$ and we say, “5 squared is 25.”
When we multiply three of the same numbers together, such as $4\boldcdot 4 \boldcdot 4$, we say we are cubing the number. We can write it like this: $$4^3$$Because $4\boldcdot 4\boldcdot 4 = 64$, we write $4^3 = 64$ and we say, “4 cubed is 64.”
We also use this notation for square and cubic units.
To read 25 in2, we say “25 square inches,” just like before.
The area of a square with side length 7 kilometers is $7^2$ km2. The volume of a cube with edge length 2 millimeters is $2^3$ mm3.
In general, the area of a square with side length $s$ is $s^2$, and the volume of a cube with edge length $s$ is $s^3$.
An expression with an exponent of 2 is sometimes called a square. The reason $s^2$ is called the square of $s$ is that a square whose edge has length $s$ has area $s^2$.
An expression with an exponent of 3 is sometimes called a cube. The reason $s^3$ is called the cube of $s$ is that a cube whose edge has length $s$ has volume $s^3$.
When we write an expression like $7^n$, we call $n$ the exponent.
