# What are we going to do? CFU Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with.

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What are we going to do? CFU Students, you already know how to evaluate squared expressions. Now, we will use squared expressions solve equations with squared variables. Make Connection Evaluate the squared expressions. 1. We will solve equations with squared variables involving fractions. 2. We will estimate radicals that are not perfect squares. Learning Objective Activate Prior Knowledge Exponential Expression An exponential expression represents repeated multiplication. Bases raised to an exponent of 2 are squared. 1. 9 2 2. 10 2 81100 3. (-9) 2 4. (-10) 2 81100 PERFECT SQUARES

Square Roots Concept Development A square root is a number that is multiplied by itself to form a product. Taking the square root ( √ ) is used to isolate 1 the variable in equations with squared variables. An equation with squared variables can have two solutions, one positive and one negative. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 x 2 = 144 √x 2 =  √12 2 x =  12 x = 12 and x = -12 both make the equation true. (12) 2 = 144(-12) 2 = 144 Solutions 1 separate (synonym) Vocabulary Which equation below can be solved by taking a square root? How do you know? A y 2 = 24 B y 2 = 16 Explain why  7 are the solutions to the equation z 2 = 49. CFU

1. a 2 = 64 2. k 2 = 144 3. q 2 = 4. p 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 interpret 2 the solution(s). Solve equations with squared variables. 1 2 3 2 explain (synonym) Vocabulary How did I/you solve the equation? How did I/you check and interpret the solution(s)? CFU 2 3 Skill Development/Guided Practice 9 25 a 2 = 8 2 a =  8 a = 8 and a = -8 both make the equation true. 8 2 = 64 (-8) 2 = 64 √a 2 =  √8 2 k 2 = 12 2 k =  12 k = 12 and k = -12 both make the equation true. 12 2 = 144 (-12) 2 = 144 √k 2 =  √12 2 q 2 = ( ) 2 3535 √q 2 =  √( ) 2 3535 q =  3535 h = and h = - both make the equation true. 3535 3535 ( ) 2 = 3535 9 25 (- ) 2 = 3535 9 25 p 2 = ( ) 2 7474 √p 2 =  √( ) 2 7474 p =  7474 h = and h = - both make the equation true. 7474 7474 ( ) 2 = 7474 49 16 (- ) 2 = 7474 49 16 A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 49 16

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 2 1 3 4 5 5. Cameron is tiling his floor with square tiles. He knows the area of each tile is 121 in 2. What is the length of each side of the tile? _________________________________________________________________________________ 6. Vanessa is starting a painting on a square canvas. The area of the canvas is 400 cm 2. What is the length of each side of the canvas? _________________________________________________________________________________ s 2 = 121 s 2 = 11 2 s =  11 11 2 = 121 (-11) 2 = 121 √s 2 =  √11 2 The length of each side of the tile is 11 in. (-11 in is not a solution because a length cannot be negative.) Area = 121 in 2 11 in Area = 400 cm 2 s 2 = 400 s 2 = 20 2 s =  20 20 2 = 400 (-20) 2 = 400 √s 2 =  √20 2 The length of each side of the canvas is 20 cm. (-20 cm is not a solution because a length cannot be negative.) 20 cm

Sometimes Square Roots are not Integers, but instead fall between integers. 1 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 Relevance A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100

What did you learn today about solving equations with squared variables? (Pair-Share) Use words from the word bank. Access Common Core Summary Closure Word Bank equation square root solution 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). Solve equations with squared variables. 1 2 3 Skill Closure 1. d 2 = 49 2. n 2 = d 2 = 7 2 d =  7 d = 7 and d = -7 both make the equation true. 7 2 = 49 (-7) 2 = 49 √d 2 =  √7 2 25 81 n 2 = ( ) 2 5959 √n 2 =  √( ) 2 5959 n =  5959 n = and n = - both make the equation true. 5959 5959 ( ) 2 = 5959 25 81 (- ) 2 = 5959 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 y 2 = 16 A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 25 81

Independent Practice 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). Solve equations with squared variables. 1 2 3 4 81 1919 g 2 = 6 2 g =  6 g = 6 and g = -6 both make the equation true. 6 2 = 36 (-6) 2 = 36 √g 2 =  √6 2 u 2 = 13 2 u =  13 u = 13 and u = -13 both make the equation true. 13 2 = 169 (-13) 2 = 169 √u 2 =  √13 2 c 2 = ( ) 2 2929 √c 2 =  √( ) 2 2929 c =  2929 c = and c = - both make the equation true. 2929 2929 ( ) 2 = 2929 4 81 (- ) 2 = 2929 4 81 v 2 = ( ) 2 1313 √v 2 =  √( ) 2 1313 v =  1313 v = and v = - both make the equation true. 1313 1313 ( ) 2 = 1313 1919 (- ) 2 = 1313 1919 A square root is 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. Perfect Squares 1 2 = 1 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 Name: ___________________ 10.31.13 4 81 1 9 1. g 2 = 36 2. u 2 = 169 3. c 2 = 4. v 2 =

Periodic Review 1 Access Common Core 1. p 2 = 1 2. x 2 = 64 3. b 2 = 4. y 2 = 1 25 36 121 p =  1 x =  8 b =  1515 y =  6 11 1. Choose Yes or No to indicate whether each statement is true about the equation p 2 = 9. AThe equation cannot be solved by taking a square root. B p  81 C p   3 DThere is more than one solution to the equation. O Yes O No 2. Choose Yes or No to indicate whether each statement is true about the equation w 2 =. AThe equation cannot be solved by taking a square root. B w  - C w   DThere are exactly two solutions to the equation. O Yes O No 3232 81 16 9494 Estimation Approximately where does fall on the number line to the right? 25 36 121 1

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