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Prentice Hall Lesson 11.4
What are like radicals? How do you combine like
radicals?
BOP:
Solution to BOP:
ALGEBRA 1 LESSON 11-3
pages 594–597 Exercises
2. 14
20. DE
6.1; EF
3.6; DF
4. 11.3
22. MN
5.1; NP
3.6; MP = 5
6. 8.1
7.6; UV
13.3
16.5;
8. 21.6
24. TU
VT
10. (–1, 12)
26. a. (20, 80), (–40, 30)
12. (–2, 3)
b. 78.1 ft
14. – 21 , –1
c. (–10, 55) or 55L10
2
16. 81 , –9
2
18. 9.4
11-3
5.7
ALGEBRA 1 LESSON 11-3
30. about 9.5 km apart
32. Yes; all sides are congruent.
34. a. about 4.3 mi
b.about 17.4 mi
11-3
Prentice Hall Lesson 11.4
What are like radicals? How do you combine like
radicals?
Toolbox:
• Like radicals in a radical expression have
the same radicand.
• Unlike radicals do not have the same
radicand.
• To simplify sums and differences, use the
Multiplication Property of Square Roots to
simplify the radical expression(s) as needed.
Then use the Distributive Property to combine
like radicals and simplify.
• To simplify products, use the Distributive
Property to multiply. (You may use FOIL if both
expressions have two terms.) Combine like
radicals and simplify.
• Conjugates are the sum and difference of the
same two terms.
• The product of two conjugates is a difference of
two squares.
•To simplify a quotient, multiply the numerator
and denominator by the conjugate of the
denominator. Continue to simplify until the
resulting expression meets the three
requirements for a radical expression in simplest
form.
• A radical expression is in simplest form
when it meets the following requirements:
1. The radicand has no perfect-square factors
other than 1.
2. The radicand has no fractions.
3. The denominator of a fraction has no radical.
ALGEBRA 1 LESSON 11-4
Simplify 4
4
3+
3=4
3+1
= (4 + 1)
=5
3
3+
3
3
3.
Both terms contain
3.
Use the Distributive Property to
combine like radicals.
Simplify.
11-4
ALGEBRA 1 LESSON 11-4
5–
Simplify 8
8
5–
45.
45 = 8
5+
9•5
9 is a perfect square and a factor of 45.
=8
5–
9•
=8
5–3
Use the Multiplication Property of
Square Roots.
Simplify 9.
= (8 – 3)
=5
5
5
5
5
Use the Distributive Property to
combine like terms.
Simplify.
11-4
ALGEBRA 1 LESSON 11-4
Simplify
5(
8 + 9) =
=
=2
5(
40 + 9
4•
8 + 9).
5
10 + 9
10 + 9
Use the Distributive Property.
5
Use the Multiplication Property
of Square Roots.
5
Simplify.
11-4
ALGEBRA 1 LESSON 11-4
Simplify (
(
6–3
6 – 3 21)( 6 + 21)
= 36 + 126 – 3 126 – 3
21)(
441
6+
21).
Use FOIL.
=6–2
126 – 3(21)
Combine like radicals and
simplify 36 and 441.
=6–2
9 • 14 – 63
9 is a perfect square factor of 126.
=6–2
9•
Use the Multiplication Property of
Square Roots.
=6–6
14 – 63
= –57 – 6
14 – 63
Simplify
14
Simplify.
11-4
9.
ALGEBRA 1 LESSON 11-4
Simplify
8
7–
=
3
7+
7+
•
3
3
8
7–
3
.
Multiply the numerator and
denominator by the conjugate
of the denominator.
=
8( 7 + 3)
7–3
Multiply in the denominator.
=
8( 7 +
4
Simplify the denominator.
= 2(
7+
=2
7+2
3)
3)
3
Divide 8 and 4 by the common
factor 4.
Simplify the expression.
11-4
ALGEBRA 1 LESSON 11-4
A painting has a length : width ratio approximately equal to the
golden ratio (1 + 5) : 2. The length of the painting is 51 in. Find the
exact width of the painting in simplest radical form. Then find the
approximate width to the nearest inch.
Define:
51 = length of painting
x = width of painting
Relate: (1 +
Write:
5) : 2 = length : width
(1 + 5) = 51
x
2
x (1 +
5) = 102
x(1 + 5) =
102
(1 + 5)
(1 + 5)
Cross multiply.
Solve for x.
11-4
ALGEBRA 1 LESSON 11-4
(continued)
x=
(1 –
102
•
(1 –
(1 + 5)
x=
102(1 – 5)
1–5
x=
102(1 –
–4
5)
x = – 51(1 –
5)
2
x = 31.51973343
5)
5)
Multiply the numerator and the
denominator by the conjugate
of the denominator.
Multiply in the denominator.
Simplify the denominator.
Divide 102 and –4 by the
common factor –2.
Use a calculator.
x 32
The exact width of the painting is – 51(1 –
2
5)
inches.
The approximate width of the painting is 32 inches.
11-4
ALGEBRA 1 LESSON 11-4
Simplify each expression.
1. 12 16 – 2
40
4. (
16
3–2
21)(
–123 + 3
7
2.
3+3
20 – 4
–2 5
21)
5
5.
3.
16
5–
–8
11-4
2( 2 + 3
2+3 6
7
5–8
7
3)
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