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