Chapter 9 Section 6

1
Chapter 9 Section 6

• Radicals Applications and Problem Solving

2
Learning Objective

• Use the Pythagorean Theorem
• Use the distance formula
• Use radicals to solve application problems

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Key Vocabulary

• Pythagorean Theorem
• distance formula

4
Radicals Application and Problem Solving

• To solve application problems you must answer the
  question asked.
• Well-labeled diagrams and pictures will help you
  understand the problem
• Five-step problem solving procedure
• Understand the Problem Identify the quantity or
  quantities you are being asked to find.
• Translate the problem into mathematical language
  (express the problem as an equation).
• Choose a variable to represent one quantity,
  write down exactly what it represents.
• Using this information write the equation that
  represents the application.
•  Carry out the mathematical calculations (solve
  the equation).
•  Check the answer (using the original
  application).
•  Answer the question asked.

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Solving Radical Equations

• Pythagorean Theorem
• The square of the hypotenuse of a right triangle
  is equal to the sum of the squares of the two
  legs
• (leg)2 (leg)2 (hypotenuse)2
• If a and b represent the legs and c represents
  the hypotenuse, then
• a2 b2 c2

c
b
When working with right triangles you should
clearly identify the hypotenuse
a
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Solving Radical Equations

• Example Find the hypotenuse of a right triangle
  whose legs are m and 5m.

c
b
a 5
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Solving Radical Equations

• Example Find the length of a diagonal of
  rectangle whose dimensions are
  45 in. by 52 in.

c
b 45
a 52
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Solving Radical Equations

• Distance Formula
• Distance formula can be used to find the
  distance between two points (x1, y1) and (x2,
  y2)
• The length of side a is x2 x1 and the length
  of side b is y2 y1

9
Solving Radical Equations

• Example Find the length of the line segment
  between the points (-1, -2) and (4, -5)

(-1,-2)x1, y1
(4,-5)x2, y2
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Solving Radical Equations

• Example Find the speed of a car that leaves a
  30 foot long skid mark. Use c 0.71
• Use the formula
• s the speed of the car
• c the coefficient of the friction and
• l the length of the longest skid

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Solving Radical Equations

• Example Find the velocity of an object that has
  dropped 16 feet
• Use the formula
• v velocity
• g acceleration due to gravity
• h height object falls
• on earth the acceleration due to gravity is 32
  ft/sec

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Solving Radical Equations

• Example Find the period (time to make swing
  back and forth) of a pendulum if its length
  is16 feet
• Use the formula
• T Time
• L length of pendulum

13
Remember

• Rule 1 - Product Rule for Square Roots
• Rule 2 Square Root of a Perfect Square
• The square root of a variable raised to an even
  power equals the variable raised to ½ that power.
  
• Rule 3 Quotient Rule for Square Roots

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Remember

• Pythagorean Theorem
• Speed Formula
• Velocity

a2 b2 c2
Distance Formula
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HOMEWORK 9.6

• Page 572 - 573
• 9, 13, 15, 19, 21, 23, 27, 29, 31, 34