11-6Radical
11-6
RadicalExpressions
Expressions
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
11-6 Radical Expressions
Warm Up
Identify the perfect square in each set.
1. 45 81 27 111 81
2. 156 99 8 25 25
3. 256 84 12 1000 256
4. 35 216 196 72 196
Holt Algebra 1
11-6 Radical Expressions
Warm Up Continued
Write each number as a product of
prime numbers.
5. 36
6. 64
7. 196
8. 24
Holt Algebra 1
11-6 Radical Expressions
Objective
Simplify radical expressions.
Holt Algebra 1
11-6 Radical Expressions
Vocabulary
radical expression
radicand
Holt Algebra 1
11-6 Radical Expressions
An expression that contains a radical sign
is a radical expression. There are many
different types of radical expressions, but in this
course, you will only study radical expressions
that contain square roots.
Examples of radical expressions:
The expression under a radical sign is the
radicand. A radicand may contain numbers,
variables, or both. It may contain one term or
more than one term.
Holt Algebra 1
11-6 Radical Expressions
Holt Algebra 1
11-6 Radical Expressions
Remember that positive numbers have two
square roots, one positive and one negative.
However,
indicates a nonnegative square
root. When you simplify, be sure that your
answer is not negative. To simplify
you
should write
because you do not
know whether x is positive or negative.
Holt Algebra 1
11-6 Radical Expressions
Example 1: Simplifying Square-Root Expressions
Simplify each expression.
A.
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B.
C.
11-6 Radical Expressions
Check It Out! Example 1
Simplify each expression.
a.
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b.
11-6 Radical Expressions
Check It Out! Example 1
Simplify each expression.
c.
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d.
11-6 Radical Expressions
Holt Algebra 1
11-6 Radical Expressions
Example 2A: Using the Product Property of Square
Roots
Simplify. All variables represent nonnegative
numbers.
Factor the radicand using perfect
squares.
Product Property of Square Roots.
Simplify.
Holt Algebra 1
11-6 Radical Expressions
Example 2B: Using the Product Property of Square
Roots
Simplify. All variables represent nonnegative
numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since x is nonnegative,
Holt Algebra 1
.
11-6 Radical Expressions
Check It Out! Example 2a
Simplify. All variables represent nonnegative
numbers.
Factor the radicand using perfect
squares.
Product Property of Square Roots.
Simplify.
Holt Algebra 1
11-6 Radical Expressions
Check It Out! Example 2b
Simplify. All variables represent nonnegative
numbers.
Product Property of Square Roots.
Product Property of Square Roots.
Since y is nonnegative,
Holt Algebra 1
.
11-6 Radical Expressions
Check It Out! Example 2c
Simplify. All variables represent nonnegative
numbers.
Factor the radicand using perfect
squares.
Product Property of Square Roots.
Simplify.
Holt Algebra 1
11-6 Radical Expressions
Holt Algebra 1
11-6 Radical Expressions
Example 3: Using the Quotient Property of Square
Roots
Simplify. All variables represent nonnegative
numbers.
A.
B.
Quotient Property
of Square
Roots.
Simplify.
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Simplify.
Quotient Property
of Square
Roots.
Simplify.
11-6 Radical Expressions
Check It Out! Example 3
Simplify. All variables represent nonnegative
numbers.
a.
b.
Simplify.
Quotient Property
of Square
Roots.
Simplify.
Holt Algebra 1
Quotient Property
of Square
Roots.
Simplify.
11-6 Radical Expressions
Check It Out! Example 3c
Simplify. All variables represent nonnegative
numbers.
Quotient Property of
Square Roots.
Factor the radicand using
perfect squares.
Simplify.
Holt Algebra 1
11-6 Radical Expressions
Example 4A: Using the Product and Quotient
Properties Together
Simplify. All variables represent nonnegative
numbers.
Holt Algebra 1
Quotient Property.
Product Property.
Write 108 as 36(3).
Simplify.
11-6 Radical Expressions
Example 4B: Using the Product and Quotient
Properties Together
Simplify. All variables represent nonnegative
numbers.
Quotient Property.
Product Property.
Simplify.
Holt Algebra 1
11-6 Radical Expressions
Check It Out! Example 4a
Simplify. All variables represent nonnegative
numbers.
Holt Algebra 1
Quotient Property.
Product Property.
Write 20 as 4(5).
Simplify.
11-6 Radical Expressions
Check It Out! Example 4b
Simplify. All variables represent nonnegative
numbers.
Holt Algebra 1
Quotient Property.
Product Property.
Write
Simplify.
as
.
11-6 Radical Expressions
Check It Out! Example 4c
Simplify. All variables represent nonnegative
numbers.
Quotient Property.
Simplify.
Holt Algebra 1
11-6 Radical Expressions
Example 5: Application
Quadrangle
250
A quadrangle on a college campus
is a square with sides of 250 feet.
If a student takes a shortcut by
walking diagonally across the
quadrangle, how far does he walk?
Give the answer as a radical
expression in simplest form. Then
estimate the length to the nearest
tenth of a foot.
250
The distance from one corner of the square to the
opposite one is the hypotenuse of a right triangle.
Use the Pythagorean Theorem: c2 = a2 + b2.
Holt Algebra 1
11-6 Radical Expressions
Example 5 Continued
Solve for c.
Substitute 250 for a and b.
Simplify.
Factor 125,000 using
perfect squares.
Holt Algebra 1
11-6 Radical Expressions
Example 5 Continued
Use the Product Property of
Square Roots.
Simplify.
Use a calculator and round
to the nearest tenth.
The distance is
Holt Algebra 1
ft, or about 353.6 feet.
11-6 Radical Expressions
Check It Out! Example 5
A softball diamond is a square
with sides of 60 feet. How long
is a throw from third base to
first base in softball? Give the
answer as a radical expression
in simplest form. Then estimate
the length to the nearest tenth
of a foot.
The distance from one corner of the square to the
opposite one is the hypotenuse of a right triangle.
Use the Pythagorean Theorem: c2 = a2 + b2.
Holt Algebra 1
11-6 Radical Expressions
Check It Out! Example 5 Continued
Solve for c.
Substitute 60 for a and b.
Simplify.
Factor 7,200 using
perfect squares.
Holt Algebra 1
11-6 Radical Expressions
Check It Out! Example 5 Continued
Use the Product Property
of Square Roots.
Simplify.
Use a calculator and round
to the nearest tenth.
The distance is
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, or about 84.9 feet.
11-6 Radical Expressions
Lesson Quiz: Part I
Simplify each expression.
1.
2.
6
|x + 5|
Simplify. All variables represent nonnegative
numbers.
3.
4.
5.
6.
Holt Algebra 1
11-6 Radical Expressions
Lesson Quiz: Part II
7. Two archaeologists leave from
the same campsite. One
travels 10 miles due north
and the other travels 6 miles
due west. How far apart are
the archaeologists? Give the
answer as a radical
expression in simplest form.
Then estimate the distance to
the nearest tenth of a mile.
mi; 11.7mi
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