Matematika Ria
Tambahkan ke favorit Tambahkan ke favorit
link Tautkan di sini
Beranda Matematika RiaBeranda

Hak cipta © 2009


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 (it equals 2), so it is not a surd!

Have a look at some more examples:

Number Simplifed As a Decimal Surd or
√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 that makes them 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")



If it is a root and irrational, it is a surd.

But not all roots are surds.