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
|√4||2||2||Not a surd|
|√¼||½||0.5||Not a surd|
|3√27||3||3||Not a 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")
- When it is a root and irrational, it is a surd.
- But not all roots are surds.