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.
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