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2.1 Find Square Roots and Compare Real Numbers Objective(s): 1. Find square roots. Unit 2 Solving Linear Equations A square garden has an area of 225 square feet. You want to know how much fencing you should buy to go around the garden without measuring. 2. Compare real numbers. Terms to KNOW Radical expression By knowing how to find square roots, you can find the side length and then determine how much fencing you should buy. radical radicand 1 say as "plus or minus" means to take the positive and negative answer Terms to KNOW the square of a number x is square root of a number x is the ex. the square of 4 is 16 the square root of 4 is 2 perfect square the square root of a number is an integer (no decimals) Examples 2 2.1 Find Square Roots and Compare Real Numbers (continued) Objective(s): 1. Find square roots. 2. Compare real numbers. Terms to KNOW integers whole numbers and their opposites rational numbers can be expressed as a fraction ex. 1, , terminating decimals decimals that "terminate" or stop ex. 1.5, 2.73, 4.0 repeating decimals decimals that have repeating #s or blocks of #s ex. 1.3, 0.6, 2.141414 irrational numbers numbers that do not repeat or stop ex. , , 3 Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Erase to reveal Check for Understanding Classify each number as real, rational, irrational, whole, or/and integer. 1. 5 2. 0.64 3. 4. 1.427427427 4 2.2 Solve Onestep equations Terms to KNOW Objective(s): 1. Solve onestep equations using addition and subtraction. inverse operations two operations that undo each other ex. addition and subtraction Solve: to determine the value of a variable To solve an equation you must isolate the variable. (Get the variable by itself!) 5 Check your work by using substitution. Check for Understanding m12=7 x+12=3 r+(2)=5 y+2=0 6 Solve x + (9) = 14 on the left side. Then write how to solve the problem on the right side. 2.2 Solving Onestep equations (cont'd) Objective(s): 1. Solve onestep equations using multiplication and division. Work How a. x+ 9 =14 a. given equation b. x + 9 = 14 +9 +9 b. c. x = 23 c. Katrina divided her photos into three albums. Each album contains 26 photos. How many photos did Katrina have to begin with? reciprocal the inverse of a number examples: reciprocal = reciprocal = reciprocal = 4x = 48 7 How would you solve these problems? x = 7 t = 6 p = 9 You can solve by multiplying by 1 or dividing by 1. 7 = m 6 8 2.3/2.4 Solve multistep Equations We would solve 2x 3 = 5 by working backword... Think Today's Objective: PEMDAS 1. Solve a multistep equation using addition, subtraction, multiplication, and division. backwards! SADMEP How do you wrap a present? How do you unwrap it? Work 2x 3 = 5 How Work How t + 21 = 14 8 9 10 11 2.5 Solve Equations with Variables on both sides Objective(s): 1. Solve equations with variables on both sides. 12 no solution- when you end up with two numbers on opposite sides of the equals sign that are not equal identity- an equation that is true for every value of the variable 13 Explain why 4x+1=4x+3 has no solution. 14