Surds Must known facts

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
3√11	3√11	2.2239800...(etc)	Surd
3√27	3	3	Not a surd
5√3	5√3	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.