Prentice Hall Lesson 11.1
How do you simplify a radical expression? What
is the multiplication property of square roots?
BOP:
Solution to BOP:
Possible Answer: The function is linear with a
slope of -2 and y-intercept of 7.
Prentice Hall Lesson 11.1
How do you simplify a radical expression? What is the
multiplication property of square roots?
Toolbox:
• Radical expressions contain a radical
• Multiplication Property of Square Roots:
For every number a ≥ 0 and b ≥ 0,
√a•b = √a • √b
• To simplify radical expressions, rewrite the
radicand as a product of perfect-square
factors and the remaining factors. Simplify by
taking the square root of the perfect-square
factors, leaving the remaining factors as the
radicand.
• You may use the product of radicals to find
perfect-square factors needed to simplify
radical expressions.
• Division Property of Square Roots:
For every number a ≥ 0 and b > 0,
√ = √a
√b
• When the denominator of the radicand is a
perfect square, it is easier to simplify the
numerator and denominator separately.
• When the denominator of the radicand is
not a perfect square, divide first, then
simplify.
• When the radicand in the denominator is
not a perfect square, you may need to
rationalize the denominator. Multiply the
numerator and denominator by the same
radical expression, making the
denominator a perfect square.
• A radical expression is in simplest radical
form when all three statements are true:
– The radicand has no perfect-square factors
other than 1.
– The radicand has no fractions.
– The denominator of a fraction has no radical.
ALGEBRA 1 LESSON 11-1
Simplify
243 =
=
=9
243.
81 • 3
81 is a perfect square and a factor of 243.
81 •
Use the Multiplication Property of Square Roots.
3
3
Simplify 81.
11-1
ALGEBRA 1 LESSON 11-1
Simplify
4x6 • 7x
28x7 =
=
4x6 •
= 2x3
7x
7x
28x7.
4x6 is a perfect square and a factor of 28x7.
Use the Multiplication Property of Square Roots.
Simplify
4x6.
11-1
ALGEBRA 1 LESSON 11-1
Simplify each radical expression.
a.
12 •
12 •
32
32 =
12 • 32
Use the Multiplication Property of
Square Roots.
=
384
Simplify under the radical.
=
64 • 6
64 is a perfect square and a factor of 384.
=
64 •
= 8
6
6
Use the Multiplication Property of
Square Roots.
Simplify
11-1
64.
ALGEBRA 1 LESSON 11-1
(continued)
b. 7
5x • 3
8x
7
5x • 3
8x = 21
40x2
Multiply the whole numbers and
use the Multiplication Property of
Square Roots.
= 21 4x2 • 10
factor of 40x2.
4x2 is a perfect square and a
= 21 4x2 • 10
Square Roots.
Use the Multiplication Property of
= 21 • 2x
Simplify
= 42x
10
10
Simplify.
11-1
4x2.
ALGEBRA 1 LESSON 11-1
Suppose you are looking out a fourth floor window 54 ft above
the ground. Use the formula d = 1.5h to estimate the distance you
can see to the horizon.
d =
1.5h
=
1.5 • 54
Substitute 54 for h.
=
81
Multiply.
=9
Simplify
81.
The distance you can see is 9 miles.
11-1
ALGEBRA 1 LESSON 11-1
Simplify each radical expression.
a.
b.
13
64
13
=
64
13
64
Use the Division Property of Square Roots.
=
13
8
Simplify
49
=
x4
49
x4
Use the Division Property of Square Roots.
64.
49
x4
7
= x2
Simplify
49 and
11-1
x4.
ALGEBRA 1 LESSON 11-1
Simplify each radical expression.
a.
120
10
120
=
10
12
Divide.
=
4•3
4 is a perfect square and a factor of 12.
=
4•
=2
3
3
Use the Multiplication Property of Square Roots.
Simplify
11-1
4.
ALGEBRA 1 LESSON 11-1
(continued)
b.
75x5
48x
75x5
=
48x
25x4
16
=
25x4
16
=
=
25 •
16
5x2
4
Divide the numerator and denominator by 3x.
Use the Division Property of Square Roots.
x4
Use the Multiplication Property of
Square Roots.
Simplify
25,
11-1
x4, and
16.
ALGEBRA 1 LESSON 11-1
Simplify each radical expression.
a.
3
7
3
=
7
=
=
3
•
7
7
7
Multiply by
7
7
to make the denominator a
perfect square.
3
7
49
3
7
7
Use the Multiplication Property of Square Roots.
Simplify
11-1
49.
ALGEBRA 1 LESSON 11-1
(continued)
Simplify the radical expression.
b.
11
12x3
11
=
12x3
11
•
12x3
3x
3x
=
33x
36x4
Use the Multiplication Property of Square Roots.
=
33x
6x2
Simplify
Multiply by
3x to make the denominator a
3x
perfect square.
11-1
36x4.
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