8.4
TRANSCRIPT
8.4 Simplify Radical Expressions
VocabularyRadical Expression – expression that contains
a radical, such as a square root, cube root, or other root.
Simplest form of a radical expression:No perfect square factors are in the radicand.No fractions are in the radicand.No radicands appear in the denominator of a
fraction.
Product Property of RadicalsThe square root of a product equals the
product of the square roots of the factors.
where and
Example 1 Use the product property of radicals
a. 32
=
16 • 2 Product property of radicals
=
16 2• Factor using perfect square factor.
=
24 Simplify.
b.
9x3=
9 • x2 • x Factor using perfect square factors.
=
x3x Simplify.
=
• •9 x2 x Product property of radicals
Example 2 Multiply radicals
=
16 Multiply.
=
2 8• Product property of radicals
=
4 Simplify.
a. 2 8•
b.
3x • x4=
Product property of radicals3x4 • x
=
Multiply.3x24
=
Product property of radicals34 • • x2
=
34x Simplify.
Example 2 Multiply radicals
c. • x37xy2 Product property of radicals
=
7xy23 • x
Multiply.
=
7x2y23
=3xy 7 Simplify.
Product property of radicals
=
x23 • 7 • • y2
Quotient Property of RadicalsThe square root of a quotient equals the
quotient of the square roots of the numerator and denominator.
where and
Example 3 Use the quotient property of radicals
a. 100
13 Quotient property of radicals=13
100
Simplify.=13
10
b. x2
7=
7
x2Quotient property of radicals
=7
xSimplify.
Rationalizing the denominatorThe process of eliminating a radical from an
expression’s denominator is called rationalizing the denominator.
Example 4 Rationalize the denominator
a. 7
5=
7
5•7
7Multiply by .
7
7
=5
Product property of radicals7
49
=5
Simplify.7
7
b.
2
3bMultiply by .
3b
3b= •
2
3b 3b
3b
Example 4 Rationalize the denominator
Product property of radicals=9b26b
Product property of radicals=6b
9 • b2
Simplify.=6b
3b
Example 5 Add and subtract radicals
a.
104 13+ 109–Commutative property= 104 – 109 + 13
Distributiveproperty= 10 + 13( )9–4
Simplify.= + 13105–
b.
48+5 3 Factor using perfect square factor.= 165 3 + • 3
Product property of radicals= 165 3 + • 3
Simplify.= 5 3 + 4 3
Example 5 Add and subtract radicals
Simplify.= 9 3
Distributive property= 3( )45 +
Example 6 Multiply radical expressions
Distributive propertya.
( )–4 205 4 5 •= – 5 20
Product property of radicals
4 5= – 100
Simplify.4 5= – 10
b.
)+7( 2 7 – 3 2 )(
Distributive property
= 7 – 3 2 )(7 + 7 – 3 2 )(2
Distributive property
= 7 )2( + 72– 3 2 )(+ • – 3 2 )(+ 27
Example 6 Multiply radical expressions
Simplify.= 1 – 142
Product property
of radicals
= 7 – 3 7 • 2 + 7 • 2 – 2 )2(3
Simplify.= 7 – + –143 14 6
8.4 Warm-Up (Day 1)1.
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8.4 Warm-Up (Day 2)1.
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