Example: What is 3 Cubed?

3 Cubed=
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= 3 × 3 × 3 = 27

Note: we compose "3 Cubed" together 33 (the little 3 way the number appears three time in multiplying)

Cubes indigenous 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 walk the other direction:

3 cubed is 27, for this reason the cube root of 27 is 3

327

The cube root of a number is ...

You are watching: What is the cube root of 30

... A distinct value that when cubed provides the original number.

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

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Note: when you watch "root" think

"I recognize the tree, yet what is the root that created it?"

In this instance the tree is "27", and also the cube root is "3".

Here are 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 know that 125 = 5 × 5 × 5 (if you use 5 three times in a multiplication girlfriend will gain 125) ...

... For this reason 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", that is the "radical" prize (used for square roots) with a tiny three to typical cube root.

See more: Do You Put A Comma After Thanks ? Period Or Comma After Thanks And Thank You

You deserve to use it like this:

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

You Can also Cube an adverse Numbers

Have a look at this:


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

So the cube root of −125 is −5

Perfect Cubes

The Perfect Cubes room the cubes that the whole numbers:


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

It is simple to occupational out the cube root of a perfect cube, yet it is really hard to occupational out other cube roots.


Example: what is the cube source 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 shot 3.2: 3.2 × 3.2 × 3.2 = 32.768Let"s try 3.1: 3.1 × 3.1 × 3.1 = 29.791

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



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


Squares and also Square RootsSurdsScientific CalculatorAlgebra index