Solving Quadratic Equations by Finding Square Roots

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Chapter 5.3

• Solving Quadratic Equations by Finding Square
  Roots

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Square Roots
• A number r is a square root of s if r2 s
• Positive numbers for s have two square roots.

• Negative numbers have no square roots.
• The symbol

• is called a radical sign.
• The number beneath the radical sign is the
  radicand.
• The expression

is a radical.
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5.3 Solving Quadratic Equations by Finding
Square Roots

• Properties of Square Roots
• Product Property

• e.g. 1

40

20
2

8
5

4
10

• e.g. 2

24

2
12

3
8

4
6

• Quotient Property

• e.g. 1

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Rationalizing a Denominator
• Mathematicians dont consider an expression
  simplified if it has a radical in the denominator

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Practice Simplifying Square Roots
• Simplify

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Solving Quadratics with radicals e.g. 1
• Solve 2x2 1 33
• - 1 -1
• ---------------
• 2x2 32
• /2 /2
• -------------
• x2 16
• x 4

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Order to solve Equations
• Subtraction
• Addition
• Division
• Multiplication
• Exponents
• Parentheses

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Solving Quadratics with radicals e.g. 2
• Solve

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Solving Quadratics with radicals e.g. 3
• Solve

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Using quadratic models in real life
• Equation of height as a function of time of an
• object in freefall

• Gravitational acceleration (g) is -9.80665 m/s2.
• Often this equation is used to find out the
  length of time it takes an object to fall to the
  ground.

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5.3 Solving Quadratic Equations by Finding
Square Roots

• Using quadratic models in real life
• Find the length of time it takes for an object to
  hit the ground if it is dropped from 10 feet.

The object will fall in about 0.791 seconds
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