# Surds

When we 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 |

√¼ | ½ | 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 |

The surds have a decimal which goes on forever without repeating: they 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 *al-Khwarizmi* (the Persian guy who we get the name "Algorithm" from) called irrational numbers "'inaudible" ... this was later translated to the Latin * surdus* ("deaf" or "mute")

## Conclusion

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