4 5 Squares and Square Roots Warm Up

4 -5 Squares and Square Roots Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

4 -5 Squares and Square Roots Warm Up Simplify. 1. 52 25 3. 122 144 5. 202 400 2. 82 64 4. 152 225

4 -5 Squares and Square Roots Problem of the Day A Shakespearean sonnet is a poem made up of 3 quatrains (4 lines each), and a couplet (2 lines). Each line is in iambic pentameter (which means it has 5 iambic feet). So, how many iambic feet long is a Shakespearean sonnet? 70

4 -5 Squares and Square Roots Sunshine State Standards MA. 8. A. 6. 2 Make reaonable approximations of square roots…, and use them to estimate solutions to problems…

4 -5 Squares and Square Roots Vocabulary square root: A number that when multiplied by itself forms a given product principal square root: The nonnegative square root of a number perfect square: A number that has integers as its square roots

4 -5 Squares and Square Roots Think about the relationship between the area of a square and the length of one of its sides. area = 36 square units side length = 6 units because 62= 36 A number that when multiplied by itself to form a product is the square root of that product. Taking the square root of a number is the inverse of squaring the number. 62 = 36 36 = 6

4 -5 Squares and Square Roots Every positive number has two square roots, one positive and one negative. The radical symbol indicates the nonnegative or principal square root. The symbol – is used to indicate the negative square root. The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Other perfect squares include 1, 4, 9, 25, 64, and 81. Caution! – 49 is not the same as – 49. A negative number has no real square root.

4 -5 Squares and Square Roots Additional Example: 1 Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number. A. 49 – 49 = 7 49 = – 7 B. 100 = 10 – 100 = – 10 C. 225 – 7 is a square root, since 7 • 7 = 49. – 7 is also a square root, since – 7 • – 7 = 49. 10 is a square root, since 10 • 10 = 100. – 10 is also a square root, since – 10 • – 10 = 100. 225 = 15 15 is a square root, since 15 • 15 = 225 = – 15 is also a square root, since – 15 • – 15 = 225.

4 -5 Squares and Square Roots Check It Out: Example 1 Find the two square roots of each number. A. 81 81 = 9 • 9 = 81 (– 9) = 81 = ± 9 B. 144 = 12 • 12 = 144 (– 12) = 144 = ± 12 C. 324 = 18 • 18 = 324 (– 18) = 324 = ± 18

4 -5 Squares and Square Roots Additional Example 2: Application A square window has an area of 169 square inches. How wide is the window? Write and solve an equation to find the area of the window. 132 = 169 So 169 = 13. Use the positive square root; a negative length has no meaning. The window is 13 inches wide. Remember! The area of a square is s 2, where s is the length of a side.

4 -5 Squares and Square Roots Check It Out: Example 2 A square window has an area of 225 square inches. How wide is the window? 152 = 225 so 225 = 15; The window is 15 inches wide.

4 -5 Squares and Square Roots Additional Example 3 A: Evaluating Expressions Involving Square Roots Simplify the expression. 3 36 + 7 = 3(6) + 7 Evaluate the square root. = 18 + 7 Multiply. = 25 Add.

4 -5 Squares and Square Roots Additional Example 3 B: Evaluating Expressions Involving Square Roots Simplify the expression. 25 + 3 16 4 25 +16 3= 4 3 1. 5625 + 4 25 =16 1. 5625. = 1. 25 + 3 4 Evaluate the square roots. =2 Add.

4 -5 Squares and Square Roots Check It Out: Example 3 A Simplify each expression. 2 121 + 9 = 2(11) + 9 = 22 + 9 = 31

4 -5 Squares and Square Roots Check It Out: Example 3 B Simplify each expression. 16 + 2 36 3 16 + 2 = 16 + 2 36 3 3 36 =4 + 2 6 3 = 4 , or 11 3 3

4 -5 Squares and Square Roots Check It Out: Example 3 C Simplify each expression. – 5 336 + 25 = – 5 361 = – 5(19) = – 95

4 -5 Squares and Square Roots Check It Out: Example 3 D Simplify each expression. 12 • 2 48 48 = 2 48 • 12 = 2 576 = 2(24) = 48

4 -5 Squares and Square Roots Lesson Quizzes Standard Lesson Quiz for Student Response Systems

4 -5 Squares and Square Roots Lesson Quiz Find the two square roots of each number. 1. 81 9 2. 2500 50 Evaluate each expression. 3. 3 16 + 1 13 4. 7 9 – 2 49 7 5. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft 2. How much fencing does she need? 45 ft

4 -5 Squares and Square Roots Lesson Quiz for Student Response Systems 1. Find two square roots of each number. 64 A. 4 B. 8 C. 9 D. 16

4 -5 Squares and Square Roots Lesson Quiz for Student Response Systems 2. Find two square roots of each number. 6400 A. 4 B. 8 C. 80 D. 800

4 -5 Squares and Square Roots Lesson Quiz for Student Response Systems 3. Evaluate the expression. A. 44 B. 17 C. 19 D. 72

4 -5 Squares and Square Roots Lesson Quiz for Student Response Systems 4. Evaluate the expression. A. 4 B. 8 C. 16 D. 40