Example: What is 3 Cubed?

3 Cubed=
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= 3 × 3 × 3 = 27

Note: we write "3 Cubed" together 33 (the small 3 means the number shows up three times in multiplying)

Cubes indigenous 03 come 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 go the various other direction:

3 cubed is 27, therefore the cube root of 27 is 3

327

The cube root of a number is ...

You are watching: What is the cube of 13

... A one-of-a-kind value that when cubed provides the original number.

The cube source of 27 is ... ... 3, since when 3 is cubed you gain 27.

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Note: once you watch "root" think

"I know the tree, yet 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:


4
64
5
125
6
216

Example: What is the Cube source of 125?

Well, we just take place to recognize that 125 = 5 × 5 × 5 (if you use 5 3 times in a multiplication friend will obtain 125) ...

... So the cube source of 125 is 5


The Cube source Symbol

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This is the one-of-a-kind symbol that means "cube root", it is the "radical" symbol (used for square roots) with a small three to typical cube root.

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You have the right to use it choose this:

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(we speak "the cube root of 27 equates to 3")

You Can also Cube an adverse Numbers

Have a look at this:


When we cube +5 we get +125:+5 × +5 × +5 = +125
When us cube −5 we get −125:−5 × −5 × −5 = −125

So the cube root that −125 is −5

Perfect Cubes

The Perfect Cubes are the cubes that the totality numbers:


PerfectCubes
00
11
28
327
464
5125
6216
7343
8512
9729
101000
111331
121728
132197
142744
153375

It is basic to occupational out the cube source of a perfect cube, but it is really hard to work-related out various other cube roots.


Example: what is the cube root of 30?

Well, 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64, therefore we have the right to guess the prize is between 3 and 4.

Let"s shot 3.5: 3.5 × 3.5 × 3.5 = 42.875Let"s try 3.2: 3.2 × 3.2 × 3.2 = 32.768Let"s shot 3.1: 3.1 × 3.1 × 3.1 = 29.791

We are acquiring closer, but an extremely slowly ... In ~ this point, I obtain out mine calculator and it says:



... However the digits simply go on and also on, without any kind of pattern. So also the calculator"s prize is only one approximation ! (Further reading: these kind of number are referred to as surds which room a special form of irrational number)


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