Download 7.3 Multiplying Radical Expression

6.3 Simplifying Radical
Expressions
In this section, we assume that all
variables are positive.
The Product Rule for Radicals
For any nonnegative real numbers a and b and
any index k,
(To multiply, multiply the radicands.)
Multiply and simplify radical expressions.
5) Multiply and simplify radical expressions.
Factoring Radical Expressions
For any nonnegative real numbers a and b and any
index k,
(Take the kth root of each factor separately.)
Simplifying kth Roots
To simplify a radical expression by factoring:
1. Look for the largest factors of the radicand that
are perfect kth powers (where k is the index).
2. Then take the kth root of the resulting factors.
3. A radical expression, with index k, is simplified
when its radicand has no factors that are perfect
kth powers.
Multiply and simplify radical expressions.
9) Simplify by factoring.
10) Multiply and simplify radical expressions.
11) Multiply and simplify radical expressions.
12) Multiply and simplify radical expressions.
The Quotient Rule for Radicals
For any nonnegative number a, any positive
number b, and any index k,
(To divide, divide the radicands. After doing this,
you can sometimes simplify by taking roots.)
13) Divide and simplify
=
14) Divide and simplify radical expressions.
For any nonnegative number a, any positive
number b, and any index k,
(Take the kth roots of the numerator and of the
denominator separately.)
15) Simplify
16) Divide and simplify radical expressions.
17) Divide and simplify radical expressions.
a
2 1

3 2
1
6
b
a b
5
6
4 1

3 2