### Example: What is 3 Cubed?

3 Cubed | = | ||

= | 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**

3 | 27 |

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) ...
## The Cube Root Symbol
(we say "the cube root of 27 equals 3")## You Can Also Cube Negative NumbersHave 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 ## Perfect CubesThe Perfect Cubes are the cubes of the entirety numbers:
It is basic to occupational out the cube root of a perfect cube, but it is ## 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 = 29.791We 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 Squares and also Square RootsSurdsScientific CalculatorAlgebra Index |