Chapter 9 Section 6 Radicals: Applications and Problem Solving

Learning Objective 1.Use the Pythagorean Theorem 2.Use the distance formula 3.Use radicals to solve application problems

Key Vocabulary Pythagorean Theorem distance formula

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: 1.Understand the Problem – Identify the quantity or quantities you are being asked to find. 2.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. 3. Carry out the mathematical calculations (solve the equation). 4. Check the answer (using the original application). 5. Answer the question asked.

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 a 2 + b 2 = c 2 c b a When working with right triangles you should clearly identify the hypotenuse

Solving Radical Equations Example: Find the hypotenuse of a right triangle whose legs are m and 5m. c a = 5 b =

Solving Radical Equations Example: Find the length of a diagonal of rectangle whose dimensions are 45 in. by 52 in. a = 52 b = 45 c

Solving Radical Equations Distance Formula: Distance formula can be used to find the distance between two points (x 1, y 1 ) and (x 2, y 2 ) The length of side a is x 2 – x 1 and the length of side b is y 2 – y 1

Solving Radical Equations Example:Find the length of the line segment between the points (-1, -2) and (4, -5) (4,-5) x 2, y 2 (-1,-2) x 1, y 1

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

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

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

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

Remember Pythagorean Theorem: Speed Formula: Velocity: a 2 + b 2 = c 2 Distance Formula:

HOMEWORK 9.6 Page : # 9, 13, 15, 19, 21, 23, 27, 29, 31, 34