Here are the basic rules of algebra for simplifying roots.
In these identities, a and b are arbitrary real numbers,
while m and n are positive integers;
however, the precise rule may depend on whether n is odd or even.
In each rule, if the right-hand side is defined,
then so is the left-hand side and the two sides are then equal.
n√0 = 0.
n√1 = 1.
n√ab =
n√a ⋅
n√b.
n√a/b =
n√a ÷
n√b.
1√a = a.
n√m√a =
mn√a.
n√an = |a|
if n is even;
n√an = a
if n is odd.
n√amn =
|a|m
if n is even;
n√amn =
am
if n is odd.
mn√an =
m√|a|
if n is even;
mn√an =
m√a
if n is odd.
Of course, you can ignore the absolute values when a ≥ 0.
This web page and the files linked from it
were written in 2015 and 2016 by Toby Bartels,
last edited on 2016 July 18.
Toby reserves no legal rights to them.
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