1 / 8

What are we going to do?

Learning Objective. 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. What are we going to do?. CFU. Activate Prior Knowledge. An exponential expression represents repeated multiplication.

cyma
Download Presentation

What are we going to do?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Learning Objective 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. What are we going to do? CFU Activate Prior Knowledge • An exponential expression represents repeated multiplication. • Bases raised to an exponent of 2 are squared. PERFECT SQUARES Evaluate the squared expressions. 1. 92 2. 102 Exponential Expression 81 100 Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with squared variables. Make Connection 3. (-9)2 4. (-10)2 81 100

  2. Concept Development • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate1 the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. CFU Which equation below can be solved by taking a square root? How do you know? A y2= 24 B y2 = 16 Explain why 7 arethe solutions to the equation z2 = 49. Square Roots x2 = 144 √x2 = √122 x = 12 Solutions (12)2= 144 (-12)2= 144 1 separate (synonym) Vocabulary x = 12 andx = -12 both make the equation true.

  3. Skill Development/Guided Practice • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. CFU How did I/you solve the equation? How did I/you check and interpret the solution(s)? Solve equations with squared variables. 2 Rewrite the numerical term as a squared expression. Solve the equation by taking the square root of both sides of the equation. Check and interpret2 the solution(s). 1 3 2 3 √k2 = √122 √a2 = √82 122 = 144 82= 64 k2 = 122 (-12)2 = 144 a2 = 82 (-8)2= 64 k = 12 and k = -12 both make the equation true. a = 8 and a = -8 both make the equation true. k = 12 a = 8 7 4 3 5 ( )2 = ( )2 = 9 25 49 16 9 25 49 16 7 4 3 5 7 4 3 5 √q2 = √( )2 p2 = ( )2 √p2 = √( )2 p =  q =  q2 = ( )2 7 4 3 5 3 5 7 4 9 25 49 16 (- )2 = (- )2 = 3 5 7 4 3 5 7 4 h = and h = - both make the equation true. h = and h = - both make the equation true. 2 explain (synonym) Vocabulary

  4. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 4 11 in √s2 = √202 √s2 = √112 5 s2 = 121 112= 121 Area = 121 in2 s2 = 112 (-11)2= 121 11 in s = 11 The length of each side of the tile is 11 in. (-11 in is not a solution because a length cannot be negative.) 20 cm s2 = 400 202= 400 s2 = 202 20 cm Area = 400 cm2 (-20)2= 400 s = 20 The length of each side of the canvas is 20 cm. (-20 cm is not a solution because a length cannot be negative.)

  5. Relevance • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. Sometimes Square Roots are not Integers, but instead fall between integers. 1 49 64 2 2 2 2 7 8 7 8 How can you estimate a square root of a number that is not a perfect square ? (Pair-Share) Square roots can have how many solutions? CFU 7 8 Between 7 and 7.5

  6. A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. Skill Closure Solve equations with squared variables. Rewrite the numerical term as a squared expression. Solve the equation by taking the square root of both sides of the equation. Check and interpret the solution(s). 1 2 3 25 81 25 Word Bank √d2 = √72 Word Bank equation square root solution 72 = 49 81 d2 = 72 (-7)2 = 49 d = 7 and d = -7 both make the equation true. d = 7 Access Common Core 5 9 ( )2 = 25 81 Which equation below can be solved by taking a square root? Explain your answer. Explain why the other equations cannot be solved by taking a square root. A x = 49 B y2 = 16 5 9 5 9 √n2 = √( )2 n2 = ( )2 n =  5 9 5 9 25 81 (- )2 = 5 9 5 9 n = and n = - both make the equation true. Summary Closure What did you learn today about solving equations with squared variables? (Pair-Share) Use words from the word bank.

  7. Independent Practice Name: ___________________ • A square rootis a number that is multiplied by itself to form a product. • Taking the square root(√ )is used to isolate the variable in equations with squared variables. • An equation with squared variables can have two solutions, one positive and one negative. 10.31.13 Solve equations with squared variables. Rewrite the numerical term as a squared expression. Solve the equation by taking the square root of both sides of the equation. Check and interpret the solution(s). 1 2 3 62 = 36 132 = 169 √u2 = √132 √g2 = √62 g2 = 62 (-6)2 = 36 u2 = 132 (-13)2 = 169 g = 6 u = 13 g = 6 and g = -6 both make the equation true. u = 13 and u = -13 both make the equation true. 4 81 1 9 4 1 1 3 2 9 ( )2 = ( )2 = 4 81 1 9 2 9 1 3 2 9 1 3 v =  √v2 = √( )2 c =  v2 = ( )2 √c2 = √( )2 c2 = ( )2 1 3 2 9 2 9 1 3 4 81 1 9 (- )2 = (- )2 = 81 9 1 3 2 9 1 3 2 9 v = and v = - both make the equation true. c = and c = - both make the equation true.

  8. Periodic Review 1 x = 8 p = 1 1 25 36 121 1 36 1. Choose Yes or No to indicate whether each statement is true about the equation p2 = 9. 2. Choose Yes or No to indicate whether each statement is true about the equation w2 = . 25 121 A The equation cannot be solved by taking a square root. B w= - C w= D There are exactly two solutions to the equation. O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No O Yes O No A The equation cannot be solved by taking a square root. B p= 81 C p=3 D There is more than one solution to the equation. Estimation Approximately where does fall on the number line to the right? Access Common Core 6 11 1 5 y =  b =  9 4 3 2 81 16

More Related