Cube root of -8

Example: What is 3 Cubed?

3 Cubed=
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= 3 × 3 × 3 = 27

Note: we create "3 Cubed" as 33 (the bit 3 implies the number shows up 3 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

327

The cube root of a number is ...

You watching: Cube root of -8

... a special value that when cubed offers the original number.

The cube root of 27 is ... ... 3, bereason as soon as 3 is cubed you obtain 27.

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Note: When you view "root" think

"I recognize the tree, however what is the root that developed it?"

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

Here are some even more cubes and also cube roots:


4
64
5
125
6
216

Example: What is the Cube root of 125?

Well, we just occur to understand that 125 = 5 × 5 × 5 (if you use 5 three times in a multiplication you will acquire 125) ...

... so the cube root of 125 is 5


The Cube Root Symbol

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This is the unique symbol that indicates "cube root", it is the "radical" symbol (supplied for square roots) via a small 3 to intend cube root.

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You have the right to use it choose this:

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(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 acquire +125:+5 × +5 × +5 = +125
When we cube −5 we gain −125:−5 × −5 × −5 = −125

So the cube root of −125 is −5

Perfect Cubes

The Perfect Cubes are the cubes of the entirety 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 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 also 4 × 4 × 4 = 64, so we deserve to guess the answer is in between 3 and 4.

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

We are gaining closer, however exceptionally slowly ... at this allude, I acquire out my calculator and also it says:



... but the digits simply go on and also on, without any kind of pattern. So even the calculator"s answer is just an approximation ! (More reading: these type of numbers are referred to as surds which are a special form of irrational number)


Squares and also Square RootsSurdsScientific CalculatorAlgebra Index