Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Simplify.
1. 52 2. 82
25
64
144
225
3. 122 4. 152
400
5. 202
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Vocabulary
square root principal square root perfect square
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Because the area of a square can be expressed
using an exponent of 2, a number with an exponent
of 2 is said to be squared. You read 32 as three
squared.
The square root of a number is one of the two
equal factors of that number. Squaring a
nonnegative number and finding the square root of
that number are inverse operations.
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A perfect square is a number whose square roots
are integers. Some examples of perfect squares
are shown in the table.
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Additional Example 1 Finding the Positive and
Negative Square Roots of a Number
Find the two square roots of each number.
A. 49
7 is a square root, since 7 7 49.
7 is also a square root, since 7 (7) 49.
The square roots of 49 are 7.
B. 100
10 is a square root, since 10 10 100.
10 is also a square root, since 10 (10)
100.
The square roots of 100 are 10.
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Check It Out! Example 1
Find the two square roots of each number.
A. 25
5 is a square root, since 5 5 25.
5 is also a square root, since 5 (5) 25.
The square roots of 25 are 5.
B. 144
12 is a square root, since 12 12 144.
12 is also a square root, since 12 (12)
144.
The square roots of 144 are 12.
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Additional Example 2 Application
A square window has an area of 169 square inches.
How wide is the window?
Find the square root of 169 to find the width of
the window. Use the positive square root a
negative length has no meaning.
132 169
The window is 13 inches wide.
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Check It Out! Example 2
A square shaped kitchen table has an area of 16
square feet. Will it fit through a van door that
has a 5 foot wide opening?
Find the square root of 16 to find the width of
the table. Use the positive square root a
negative length has no meaning.
So the table is 4 feet wide, which is less than 5
feet, so it will fit through the van door.
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Additional Example 3 Finding the Square Root
of a Monomial
Simplify the expression. A.
144c2
Write the monomial as a square.
Use the absolute-value symbol.
12c
B.
z6
Write the monomial as a square z6 (z3)2
z3
Use the absolute-value symbol.
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Additional Example 3 Finding the Square Root
of a Monomial
Simplify the expression. C.
100n4
Write the monomial as a square.
10n2 is nonnegative for all values of n. The
absolute-value symbol is not needed.
10n2
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Check It Out! Example 3
Simplify the expression. A.
121r2
Write the monomial as a square.
Use the absolute-value symbol.
11r
B.
p8
Write the monomial as a square p8 (p4)2
p4
Use the absolute-value symbol.
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Check It Out! Example 3
Simplify the expression. C.
81m4
Write the monomial as a square.
9m2 is nonnegative for all values of m. The
absolute-value symbol is not needed.
9m2
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Lesson Quiz
12
50
7p3
z4
5. Ms. Estefan wants to put a fence around 3
sides of a square garden that has an area of 225
ft2. How much fencing does she need?
45 ft