8 th grade math. to understand cube roots, first, you must understand cubes…… how to cube a...

Cubes and Cube Roots

8th grade math

To understand cube roots, first, you must understand cubes……

HOW TO CUBE A NUMBER:

To cube a number, just multiply a number by itself 3 times.

3 cubed = 33 = 3 x 3 x 3 = 27

3

3 3

Some more examples of cubes:

4 cubed = 43 = 4 x 4 x 4 =

1255 cubed = 53 = 5 x 5 x 5 =

64

2166 x 6 x 6 = 6 cubed = 63 =

CUBE ROOT: Just like square roots are the opposite of squaring a number,cube roots, are the opposite of cubing a number.

A cube root goes in the other direction:

3 cubed (33 ) is 27, so the cube root of 27, is 3.

CUBE

CUBE ROOT 3 2

7

The cube root of a number is………

A special value that when CUBED, gives the original number.

The cube root of 27 is 3, because…… when 3 is cubed, you get 27!

When you think of root, think…..

I know the tree, but what is the rootthat produced it?

In this case, the tree is 27, and the cube root is 3.

DO SOME EXAMPLES:

What is the cube root of 125?

What is the cube root of 512?

What is the cube root of 1,000?

5

8

10

The Cube Root Symbol!!

This is the special symbol that means ‘cube root’.

It is the RADICAL symbol (used for square roots also), with a little three to mean cube root.

This would be said, the cube root of 27 equals 3.

You can also cube negative numbers !!!

Have a look at this:

If you cube 5, you get 125: 5 x 5 x 5 = 125

If you cube -5, you get -125.

-5 x -5 x -5 = -125

So…… -125 is -5.

125 is 5.

These are some of the PERFECT CUBES of whole numbers!

While it is pretty easy to work out the cube root of a perfect cube,it is really difficult to work out other cube roots.

EXAMPLE: What is the cube root of 30?

Well, 3 x 3 x 3 = 27, and 4 x 4 x 4 = 64 ……so we know it must be in-between 3 and 4!!

GET OUT YOURCALCULATORS!

• Let’s try 3.5 X 3.5 x 3.5 42.875

• Let’s try 3.2 X 3.2 x 3.2 32.768

• Let’s try 3.1 X 3.1 x 3.1 29.791

We are getting closer, but very slowly! So, at this point, we canput it into the calculator………..

And we will get 3.1072325059538588668776624275224……

But, the digits just go on and on, without any pattern!

So, even the calculator's answer is only an approximation.

These kind of numbers are called…….

IRRATIONAL NUMBERS!!!!!!!