122 SQUARE ROOTS

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12-2 SQUARE ROOTS

• Define
• Square Root
• Radical Expression
• Radical Sign
• Principal Square Root
• Radicand

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• B. Find the square root
• Make a factor tree
• Remove pairs
• C. Examples

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12-3 THE PYTHAGOREAN THEOREM

• Define
• Right triangle
• Leg
• Hypotenuse
• Pythagorean theorem

hypotenuse
leg
leg
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• B. Find the missing side
• 1. a16 b30
• 2. a c7
• 3. b4 c5
• C. Is it a right triangle?
• - Plug into the Pythagorean theorem
• 12, 11, 15

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12-4 REAL NUMBERS

• Define
• Natural Numbers
• Whole numbers
• Integers
• Rational numbers
• Irrational numbers

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• B. Completeness Property
• C. Approximate the square root
• Using a calculator
• Using a chart (P.645)

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12-5 SIMPLIFYING SQUARE ROOTS

• Properties
• Simplified form
• No perfect squares
• No fractions
• No square root denominators

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C. Examples
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• D. Hints
• Reduce the fraction
• Split the fraction
• Multiply by
• Factor

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12-6 ADDING AND SUBTRACTING RADICAL EXPRESSIONS

• Review
• 5x 8x 3. 2x 3y
• 3x 5y x 6

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• B. Adding and subtracting
• Simplify radical
• Must have like radicals
• /- coefficients
• Keep the like radical

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C. Examples
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12-7 RADICAL EQUATIONS

• Steps
• Get
• Square both sides
• Solve
• Note
• If so No solution

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B. Examples
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12-8 THE DISTANCE FORMULA

• Formula
• Examples
• (2, 2) (5, -1)
• (9, -2) (3, -6)