# How do you simplify: square root of 1/3?

Algebra

Usually the final answer is written as ##sqrt{3}/3##

To get the final answer, you need to “rationalize the denominator” by multiplying by ##1=sqrt{3}/sqrt{3}## as follows:

##sqrt{1/3}=sqrt{1}/sqrt{3}=1/sqrt{3}=1/sqrt{3} * sqrt{3}/sqrt{3}=sqrt{3}/3##

It is **not** “mathematically illegal” to write this number as ##1/sqrt{3}## (it’s not like dividing by zero or something), but the standard convention is to avoid roots in denominators, if possible. This is done for two main reasons:

1) It helps teachers check your answers more easily.

2) Rationalizing the denominator (or numerator, for that matter) is a useful skill that can help you solve problems in higher math. For instance, in calculus, it’s a trick that can often help you solve some problems about “limits”.