## Mental Math - Cubed Roots

Mental math tricks to do perfect cube roots in your head for the integers 0 to 100.

Integer |
Cube |

1 |
1 |

2 |
8 |

3 |
27 |

4 |
64 |

5 |
125 |

6 |
216 |

7 |
343 |

8 |
512 |

9 |
729 |

10 |
1000 |

To find the integer cube root of a number up to 6 digits (AKA a cube root of any integer 1 to 99) in your head, memorize the cubes of the integers 1 through 9 shown in the table above and the steps below.

1) The tens digit of the mysters root can be found by knocking of the last 3 numbers of the given cube and seeing where it falls within the memorized table above. The tens digit is the number corresonding to cube that is just smaller than the truncated number.

2) The ones digit can be found by taking the last digit of the given cube and finding the cube of that digit (again using the memorized table). The last digit of this new cube is the ones digit of the original mystery cubed root.

Example: What is the cube root of 389,017?

1) 390,017 -> 390 (when you remove last 3 digits) -> Which is less than 8^3(=512) and greater than 7^3(=343). This means that the tens digit is 7.

2) The last digit of the cube is 7 -> 7^3 = 343 -> The last digit of 343 is 3. This means that the ones digit is 3.

The answer is 73. The cubed root of 389,017 is 73.