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:

NumberSimplifiedAs a DecimalSurd or
not?
221.4142135...(etc)Surd
331.7320508...(etc)Surd
422Not a surd
¼½0.5Not a surd
3113112.2239800...(etc)Surd
32733Not a surd
53531.2457309...(etc)Surd

The surds have a decimal which goes on forever without repeating, and are Irrational Numbers.

scrollIn 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