# Root Calculator

## How to Calculate a Root?

Calculating the root of a number typically involves finding a value that, when raised to a certain power, results in the original number. The most common roots are square roots (finding a number that, when squared, equals the original number) and cube roots (finding a number that, when cubed, equals the original number). Here are the basic steps to calculate these roots:

### 1. Square Root (2nd root):

- To find the square root of a number, you can use the square root symbol (√) or a calculator.
- If you want to calculate the square root of a number manually, you can use the following formula:
- Given a number x, the square root (√x) is equal to x raised to the power of 0.5: √x = x^0.5

- For example, to calculate the square root of 16:√16 = 16^0.5 = 4

*square root* = 16^{0.5} = 4

### 2. Cube Root (3rd root):

- To find the cube root of a number, you can use the cube root symbol (∛) or a calculator.
- If you want to calculate the cube root manually, you can use the following formula:
- Given a number x, the cube root (∛x) is equal to x raised to the power of 1/3: ∛x = x^(1/3)

- For example, to calculate the cube root of 8:∛8 = 8^(1/3) = 2

*cube root* = ^{3}√*8* = 8^{(1/3)} = 2

### 3. Nth Root (n-th root):

- To calculate the nth root of a number, you can use the following formula:
- Given a number x and the desired root n, the nth root (∛n) is equal to x raised to the power of 1/n:∛n = x^(1/n)

- For example, to calculate the 4th root of 16: 4√16 = 16^(1/4) = 2

*nth root* = ^{4}√*16* = 16^{(1/4)} = 2

It's important to note that not all roots will result in real numbers. For instance, the square root of a negative number is a complex number. When dealing with complex roots, you may need to use complex number arithmetic.

In practice, most people use calculators or computer software to calculate roots of numbers, as it can be more efficient and accurate for large or non-integer values.

#### Square roots table

Number (x) | Square Root (√n) |
---|---|

1 | 1 |

2 | 1.414 |

3 | 1.732 |

4 | 2 |

5 | 2.236 |

6 | 2.449 |

7 | 2.646 |

8 | 2.828 |

9 | 3 |

10 | 3.162 |

11 | 3.317 |

12 | 3.464 |

13 | 3.606 |

14 | 3.742 |

15 | 3.873 |

16 | 4 |

17 | 4.123 |

18 | 4.243 |

19 | 4.359 |

20 | 4.472 |

See also