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 | Simplified | 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, and are 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.