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Algebra
9.1 Square Roots
I will use the inverse of perfect squares to find approximate values of square roots.I will use square roots to evaluate radical expressions and solve equations.
Algebra
Objective
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Algebra
9.1 Square Roots
Vocabulary• Square root - a number n such that if
multiplied by itself, it is equal to a perfect square
- n2 = x, where x is a perfect square
- the inverse of squaring a number
- all positive numbers have two square roots (1 positive, 1 negative)
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Algebra
9.1 Square Roots
Vocabulary• Perfect square - a number that is a square of
an integer
- Examples: 1, 4, 9, 16, 25…
• Radicand - the number or expression inside a radical symbol
• Irrational Number - a number that cannot be written as the quotient of two integers (example: square roots)
• Radical Expression - an expression with a square root (or radical)
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Algebra
9.1 Square RootsThink about the relationship between the area of a square and the length of one of its sides.
Taking the square root of a number is the inverse of squaring the number.
area = 36 square unitsside length = 36 = 6 units
62 = 36 36 = 6
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Algebra
9.1 Square Roots
–49 is not the same as – 49. A negative number has no real square root.
Caution!
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Algebra
9.1 Square Roots
A. 255 is a square root, since 5 • 5 = 25.–5 is also a square root, since –5 • –5 = 25.Rewrite as
12 is a square root, since 12 • 12 = 144.
–12 is also a square root, since –12 • –12 = 144.Rewrite as
Find the two square roots of each number.
B. 144
25 5
5
144 12
12
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Algebra
9.1 Square Roots
A. 49
Guided PracticeFind the two square roots of each number.
B. 225
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Algebra
9.1 Square Roots
132 = 169
The window is 13 inches wide.
Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning.
Example 2: ApplicationA square window has an area of 169 square inches. How wide is the window?
So 169 = 13.
The area of a square is s2, where s is the length of a side.
Remember!
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Algebra
9.1 Square Roots
Approximating a Square Root
• To approximate a square root
- choose one perfect square less than the number and one perfect square greater than the number
- take the square root of the perfect square of that is nearest to the original number
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Algebra
9.1 Square Roots
Example 3: Approximating a Square Root
Find the square root of 78.
64 < 78 < 81 Identify the perfect squares closest to 78
78 is closer to 81 than 64.
Find the square root of 81
81 9
78 9
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Algebra
9.1 Square Roots
Guided Practice
Find the square root of 135.
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Algebra
9.1 Square Roots
Lesson Quiz
Find the two square roots of each number.
1. 81 2. 25009 50