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

1 Answer
Bill K.
Jul 24, 2015

Usually the final answer is written as √33

Explanation:

To get the final answer, you need to "rationalize the denominator" by multiplying by 1=√3√3 as follows:

√13=√1√3=1√3=1√3⋅√3√3=√33

It is not "mathematically illegal" to write this number as 1√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".

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