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
|√4||2||2||Not a surd|
|√(1/4)||1/2||0.5||Not a surd|
|3√(27)||3||3||Not a 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")
- If it is a root and irrational, it is a surd.
- But not all roots are surds.