Page 706 - Algebra 1

L E S S O N Dividing Radical Expressions 103
Warm Up
New Concepts
1. Vocabulary The number or expression under a radical symbol is called
(13)
Simplify. All variables represent non-negative numbers.
the __________.
2. √ 15 0 (61)
4. √ 48 x3 (61)
3. 3√ 72 (61)
5. √ 12 · √ 15 (76)
When dividing radical expressions, use the Quotient Property of Radicals.
_
_a
√n = √n a ,whereb≠0.
b

Math Language
In the expression √n _a , _a b
b is the radicand and n is the index number.
n √ b
A radical expression in simplest form cannot have a fraction for a radicand or a radical in the denominator. To rationalize a denominator means to use a method which removes radicals from the denominator of a fraction. Using this method, a fraction is multiplied by another fraction that is equivalent to 1 in order to remove the radical from the denominator.
Example
1
Rationalizing the Denominator
Simplify.
√ 7 _
3
SOLUTION
Use the quotient property. Then rationalize the denominator.
Math Reasoning
_ Verify Multiply √ 21
_3
b y √ 3 t o s h o w t h a t √3
the product equals the
_ original expression √ 7 . √ 3
√ 7 _
3 _
= √7 √3
Quotient Property of Radicals
Multiply the expression by a factor of 1 that will make the radicand in the denominator a perfect square.
Multiplication Property of Radicals Multiply.
Simplify the square root.
= √7 · √3 __
_√3 √3
= √7 · 3 √3 · 3
= _√2 1 √9
= _√2 1 3
Lesson 103 691