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Indices: Squares and Cubes

# Indices: Squares and Cubes

### Indices: Squares and Cubes

You can multiply a number by itself infinite times, where the number of multiplications is called the power. The most common powers are called squares and cubes.

1

To get started, what is this shape?

2

And would you calculate the area of this square?

3

True or false? The width and the height will always be the same length in a square.

4

You can also write $3 \times 3$ as $3^2$

You read $3^2$as "3 to the power of 2" or "3 squared", because it equals the area of a square whose sides are length $3$

5

So $3 \times 3$ and $3^2$ (3 squared) is the same. What does $3^2$ equal?

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The area of the square, whose sides are length $3$, equals $9$

So $3 \times 3$ or $3^2$ (3 squared) equals $9$

1

The little $^2$ in $4^2$ is called the power

You can also say "4 to the power of 2". Numbers that are raised to powers, like $4^2$, are called indices. Sometimes, the power is also called the index.

2

What does $4^2$ (4 squared) equal?

What does $1^2$ (one squared) equal?

What does $5^2$ (5 squared) equal?

1

Now what is this shape?

2

How do you calculate the volume of this cube?

3

So you would calculate the volume of this cube like $2 \times 2 \times 2$. How do you think you can also write that?

4

You can also read $2^3$ as "2 __________".

5

$2^3$ essentially represents the volume of a cube

So you can read $2^3$ as "2 cubed".

1

What does $3^3$ (3 cubed) equal?

1

What does $1^3$ (1 cubed) equal?

What does $5^3$ (5 cubed) equal?

What does $4^3$ (4 cubed) equal?

1

Summary! You can "square" a number

This means you multiply it by itself, like when you find the area of a square.

2

For example $3^2$ (3 squared) equals $9$

This is because $3 \times 3=9$

3

You can also "cube" a number

This means you multiply it by itself 3 times, like when you find the volume of a cube.

4

For example $3^3$ (3 cubed) equals $27$

This is because $3 \times 3 \times 3=27$

5

Numbers like $4^2$ or $5^3$ are called indices

You say "one index" and "many indices".

6

The little $^2$ in $4^2$ and the little $^3$ in $5^3$ are called powers or indices.

You can also say "4 to the power of 2" and "5 to the power of 3".