Exponents And Radicals Worksheets Page 10
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15Radicals and Their Properties
n ≥
Definition:
Let a and b be real numbers with
a positive
2
=
n
a
b
integer. If
, then b is the nth root of a.
n = 2
Square root
n = 3
Cube root
Definition:
Let a be a real number that has at least one nth root.
The principal nth root of a is the nth root that has the same sign
as a. It is denoted by a radical symbol.
n
a
The positive number n is the index of the radical, and the number
a is the radicand. If n = 2, omit the index.
Some perfect squares: 1, 4, 9, 16, …, 81, 100, …
Some perfect cubes:
1, 8, 27, 64, …, 729, 1000, …
Properties of Radicals (p. 16)
=
n
m
m
n
1.
a
(
a
)
=
n
n
n
2.
a b
ab
n
a
a
=
≠
3.
,
b
0
n
n
b
b
=
m n
mn
4.
a
a
=
n
n
5.(
a
)
a
=
n
n
6.
a
a even
,
=
n
n
a
a odd
,
M161c1s2p2
10
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