Simplifying roots
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√(a(mn)) =
|a|m
if n is even;
n√(a(mn)) =
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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This web page was written in 2015 by Toby Bartels, last edited on 2015 July 27.
Toby reserves no legal rights to it.
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