 State whether or not the given statements are true or false. If true, give two examples using real numbers to show. If false, provide one counterexample. When you have written down your answer, discuss with your desk partner.

 Objectives: Find the roots of real numbers.  Vocabulary: Principal square root- the positive square root of a number  Homework:  Tools and Rules: 1.No radicand contains a factor (other than 1) that is a perfect nth power. 2. No radicals in denominator. p. 262 (Written) #2- 20 evens

 Find the prime factorization of the following numbers. (List the prime factors in increasing order)  1) 18  2) 75  3) 32  4) 220  5) 176

 Objectives: Simplify expressions involving radicals.  Vocabulary: Simplest Radical Form: 1. No perfect nth powers left in radicand. 2. No radical in denominator (rationalized). Rationalizing the denominator: Multiply numerator and denominator of a fraction to get rid of a radical in the denominator.  Examples: See board  Tools and Rules: Product Property of Radicals: Quotient Property of Radicals: Two Theorems: Homework: P. 267 #2-30 evens ; all

 Simplify the following: Answer this question.

 Objectives: Simplify expressions involving sums of radicals..  Vocabulary:  Like radicals: Two radicals with the same index and radicand. (Solve like combining like terms).  Ex: 3x + 5x = 8x  3√2 + 5√2 = 8√2  Homework: P. 272 #2-26 evens,  Tools and Rules:

 Turned-in

 Objectives: Multiplying binomials containing radicals  Vocabulary:  Binomial: Polynomial with two terms.  Conjugate: Expressions of the form a√b + c√d and a√b – c√d  Homework: P. 275 #1-16 all  Tools and Rules:  Conjugates are used to rationalize denominators: P. 272 #2-26 evens, 35+36

 Investigators are looking into the scene of a car accident. There are long skid marks on the road. They are trying to find how fast a car was going when the driver hit the breaks. On dry pavement, the speed s in miles per hour is given by the following equation: s =  If the measure of the skid marks was 100 ft, then how fast was the car going?  We can also use this formula to find the breaking distance of a car given speed.  What is the breaking distance required for a car traveling at 40 mph? Warm-Up 11/14

 Objectives: Solving equations involving radicals.  Vocabulary: Extraneous Roots: A solution that’s NOT a solution of the original equation.  Homework:  Tools and Rules:  Solve radical equations by isolating the radical and squaring (or cube if cubed root) both sides of the equation. P. 280 #1-14 all, 20

 Objectives: Use the number i to simplify square roots with negative numbers.  Vocabulary: pure imaginary numbers: numbers that have the form bi (a real number times i).  Homework:  Tools and Rules:  √-r = i √r P. 290 #2-30 evens

 Objectives: Adding, subtracting, and multiplying complex numbers.  Vocabulary: Complex number-A number of the form a + bi where a and b are real numbers.  Homework: P. 295 #1-6 all  Tools and Rules: a + bi = c + di if and only if a = c and b = d. Addition: (a + bi) + (c + di) = (a + c) + (b + d)i * *when subtracting, distribute the negative sign, then add. Multiplication: (a + bi)(c+ di) = (ac – bd) + (ad + bc)i

 Solve

 Objectives: Multiplying and Dividing complex numbers.  Vocabulary: Conjugate: See notes from 6.4  Homework:  P. 295 #8-40 evens  Tools and Rules: Multiplication: (a + bi)(c+ di) = (ac – bd) + (ad + bc)i Division: Use conjugates. Conjugate of a + bi is a - bi

 Solve

 Objectives: Graphing complex numbers.  Vocabulary: Vector- a line that shows magnitude (size or length) and direction.  Homework:  See school fusion for worksheet  Tools and Rules: X-axis = Real numbers Y-axis = Imaginary numbers A complex number a + bi can be graphed as the point (a, b) or the vector from the origin to the point (a, b).