Warm-Up

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Warm-Up

• Find the Square Root
• 1) 3)
• 2) 4)

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Objectives
Estimate square roots. Simplify square roots.
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• The side length of a square is the square root
  of its area. This relationship is shown by a
  radical symbol . The number or expression
  under the radical symbol is called the radicand.
  The radical symbol indicates only the positive
  square root of a number, called the principal
  root. To indicate both the positive and negative
  square roots of a number, use the plus or minus
  sign ().

or 5
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Example 1 Estimating Square Roots
Estimate to the nearest tenth.
Find the two perfect squares that 27 lies between.
Find the two integers that lies between
.
Try 5.2 5.22 27.04
Too high, try 5.1.
5.12 26.01
Too low
Check On a calculator 5.1961524
5.2 rounded to the nearest tenth.
?
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Check It Out! Example 1
Estimate to the nearest tenth.
Find the two perfect squares that 55 lies
between.
Find the two integers that lies between
.
Try 7.2 7.22 51.84
Too low, try 7.4
7.42 54.76
Too low but very close
Check On a calculator 7.4161984
7.4 rounded to the nearest tenth.
?
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• Numbers such as 25 that have integer square
  roots are called perfect squares. Square roots of
  integers that are not perfect squares are
  irrational numbers. You can estimate the value of
  these square roots by comparing them with
  perfect squares. For example, lies between
  and , so it lies between 2 and 3.

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Square roots have special properties that help
you simplify, multiply, and divide them.
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Example 2 Simplifying SquareRoot Expressions
Simplify each expression.
A.
Find a perfect square factor of 32.
Product Property of Square Roots
B.
Quotient Property of Square Roots
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Check It Out! Example 2
Simplify each expression.
A.
Find a perfect square factor of 48.
Product Property of Square Roots
B.
Quotient Property of Square Roots
Simplify.
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Example 3B Rationalizing the Denominator
Simplify the expression.
Multiply by a form of 1.
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Check It Out! Example 3a
Simplify by rationalizing the denominator.
Multiply by a form of 1.
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Check It Out! Example 3b
Simplify by rationalizing the denominator.
Multiply by a form of 1.
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Homework!

• Holt 1.3
• p. 24
• 1-13, 18-33

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