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
311 311 2.2239800...(etc) Surd
327 3 3 Not a surd
53 53 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.