# Surds

If you can't simplify a number to remove a square root (or cube root etc) then it is a surd.

Example: √2 (square root of 2) can't be simplified further so it is a **surd**

Example: √4 (square root of 4) **can** be simplified (to 2), so it is **not a surd**!

Have a look at some more examples:

Number | Simplifed | As a Decimal | Surd or not? |
---|---|---|---|

√2 | √2 | 1.4142135...(etc) | Surd |

√3 | √3 | 1.7320508...(etc) | Surd |

√4 | 2 | 2 | Not a surd |

√(1/4) | 1/2 | 0.5 | Not a surd |

^{3}√(11) |
^{3}√(11) |
2.2239800...(etc) | Surd |

^{3}√(27) |
3 | 3 | Not a surd |

^{5}√(3) |
^{5}√(3) |
1.2457309...(etc) | Surd |

As you can see, the surds have a decimal which goes on forever without repeating, and are actually Irrational Numbers.

In fact "Surd" used to be another name for "Irrational", but it is now used for a root that is irrational. |

How did we get the word "Surd" ? Well around 820 AD |

## Conclusion

- If it is a
**root**and**irrational**, it is a surd. - But
**not all**roots are surds.