Example: What is 3 Cubed?

3 Cubed=
*
= 3 × 3 × 3 = 27

Note: we write "3 Cubed" as 33 (the small 3 method the number appears three times in multiplying)

Cubes from 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 goes the other direction:

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

327

The cube source of a number is ...

You are watching: 1 cubed 2 cubed 3 cubed

... 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 acquire 27.

*

Note: once you view "root" think

"I understand the tree, but what is the source that created it?"

In this case the tree is "27", and also the cube source is "3".

Here space some much more cubes and also cube roots:


4
64
5
125
6
216

Example: What is the Cube source of 125?

Well, us just occur to understand that 125 = 5 × 5 × 5 (if you usage 5 three times in a multiplication you will obtain 125) ...

... Therefore the cube source of 125 is 5


The Cube root Symbol

*

This is the special symbol that method "cube root", that is the "radical" price (used for square roots) through a tiny three to mean cube root.

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You can use it favor this:

*
(we speak "the cube source of 27 amounts to 3")

You Can likewise Cube an unfavorable Numbers

Have a look at this:


When us cube +5 we obtain +125:+5 × +5 × +5 = +125
When we cube −5 we acquire −125:−5 × −5 × −5 = −125

So the cube root the −125 is −5

Perfect Cubes

The Perfect Cubes are the cubes that the entirety numbers:


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

It is simple to job-related out the cube source of a perfect cube, yet it is really hard to job-related out various other cube roots.


Example: what is the cube root of 30?

Well, 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64, for this reason we have the right to guess the prize is in between 3 and 4.

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

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



... Yet the digits simply go on and also on, without any kind of pattern. So also the calculator"s answer is only an approximation ! (Further reading: these sort of number are dubbed surds which room a special type of irrational number)


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