For cube roots of 1000, the following simple procedure should be followed:

Factorize 1000 in the following manner.

2 | 1000 |

2 | 500 |

2 | 250 |

5 | 125 |

5 | 25 |

5 | |

You should ensure that each time you factorize 1000 with the lowest multiple of resultant in each step. For example if 500 is divisible by both 5 and 2, you should go for 2 which is the lowest multiple of 500.

The second steps involves the listing of all the multiples of 1000 in ascending order in the following way:

2,2,2,5,5,5

Now rewrite the above numbers in their cubical forms as unders:

2^3, 5^3

Now simply cancel out the cubes and the product of the resultant would be the cubic under root of 1000 ie 5x2=10.

Here it is worth nothing that while canceling out the cubes make sure that you only cancel out the cubes and let the remaining numbers as it is.

Another point worth remembering is that when you are calculating fourth roots of a number make sure that you following the similar procedure as summarized below.

Firstly simplify the number by its lowest multiples.

Then arrange the multiples in their ascending order.

Then write them in their fourth root forms.

Then cancel out their fourth roots.

Then multiply the multiples after removing their fourth roots.

The result will give you the fourth roots of that number.

You can practice this exercise to find out the roots of any number.