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 (to 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.