lesson cube and cube root
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Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
How to Cube A Number
To cube a number, just use it in a multiplication 3 times ...
Example: What is 3 Cubed?
3 Cubed = cube 3x3x3
= 3 × 3 × 3 = 27
Note: we write "3 Cubed" as 33
(the little 3 means the number appears three times in multiplying)
Cubes From 03 to 63
0 cubed = 03 = 0 × 0 × 0 = 0
1 cubed = 13 = 1 × 1 × 1 = 1
2 cubed = 23 = 2 × 2 × 2 = 8
3 cubed = 33 = 3 × 3 × 3 = 27
4 cubed = 43 = 4 × 4 × 4 = 64
5 cubed = 53 = 5 × 5 × 5 = 125
6 cubed = 63 = 6 × 6 × 6 = 216
Cube Root
A cube root goes the other direction:
3 cubed is 27, so the cube root of 27 is 3
3 cube root direction 27
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.
tree root
Note: When you see "root" think
"I know the tree, but what is the root that produced it?"
In this case the tree is "27", and the cube root is "3".
Here are some more cubes and cube roots:
cube root direction
4
64
5
125
6
216
Example: What is the Cube root of 125?
Well, we just happen to know that 125 = 5 × 5 × 5 (if you use 5 three times in a multiplication you will get 125) ...
... so the cube root of 125 is 5
The Cube Root Symbol
cube root symbol
This is the special symbol that means "cube root", it is the "radical" symbol (used for square roots) with a little three to mean cube root.
You can use it like this: cube root 27 = 3 (we say "the cube root of 27 equals 3")
You Can Also Cube Negative Numbers
Have a look at this:
When we cube +5 we get +125: +5 × +5 × +5 = +125
When we cube −5 we get −125: −5 × −5 × −5 = −125
So the cube root of −125 is −5
Perfect Cubes
The Perfect Cubes are the cubes of the whole numbers:
Perfect
Cubes
0 0
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000
11 1331
12 1728
13 2197
14 2744
15 3375
It is easy to work out the cube root of a perfect cube, but it is really hard to work out other cube roots.
Example: what is the cube root of 30?
Well, 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64, so we can guess the answer is between 3 and 4.
Let's try 3.5: 3.5 × 3.5 × 3.5 = 42.875
Let's try 3.2: 3.2 × 3.2 × 3.2 = 32.768
Let's try 3.1: 3.1 × 3.1 × 3.1 = 29.791
We are getting closer, but very slowly ... at this point, I get out my calculator and it says:
3.1072325059538588668776624275224...
... but the digits just go on and on, without any pattern. So even the calculator's answer is only an approximation !
(Further reading: these kind of numbers are called surds which are a special type of irrational number)