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Squares and Square Roots 4-5 Warm Up on warm up paper: Homework Textbook 7.1 pg 292 # 1-3, 9 – 13, 18-23 Solve and graph 2x - 3 > 19 Use order of operations to simplify: 2 – (-4 ⅔) ∙ -1 ⅜ Find the measure of the exterior angles:

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Squares and Square Roots 4-5

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Challenge of the Week 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?

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Grade:

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Vocabulary square root principal square root perfect square

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Learn to find square roots.

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Think about the relationship between the area of a square and the length of one of its sides. A number that when multiplied by itself to form a product is the square root of that product. Every positive number has two square roots, one positive and one negative. Taking the square root of a number is the inverse of squaring the number. area = 36 square units side length = 36 = 6 units 6 2 = 36 36 = 6

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Radical Sign: Radicant: # inside the –49 is not the same as – 49. A negative number has no real square root. Caution! Positive Square Root: 16 or -16= 4 Negative Square Root: – 16 = -4 Both Square Roots: –+ 16 = -+4

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The numbers 16, 36, and 49 are examples of perfect squares. A perfect square is a number that has integers as its square roots. Ex:1, 4, 9, 25, 64, and 81

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A. 25 5 is a square root, since 5 5 = 25. –5 is also a square root, since –5 –5 = 25. 12 is a square root, since 12 12 = 144. –12 is also a square root, since –12 –12 = 144. 25 = –5 – 25 = 5 144 = 12 144 = –12 – Find the two square roots of each number. B. 144 C. 289 289 = –17 – –17 is also a square root, since –17 –17 = 289. + + +

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13 2 = 169 Use the positive square root; a negative length has no meaning. The window is 13 inches wide. Write and solve an equation to find the area of the window. A square window has an area of 169 square inches. How wide is the window? So 169 = 13. The area of a square is s 2, where s is the length of a side. Remember!

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Simplify the expression. Evaluate the square root. Add. = 25 Multiply. = 18 + 7 3 36 + 7 3 36 + 7 = 3(6) + 7

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Simplify the expression. - + 25 16 3434 3434 + 3434 = + 1.5625 Evaluate the square roots. = -1.25 + 3434 25 16 = 1.5625. = 1/2 Add. - +

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Check It Out: Example 3B Simplify the expression. + 18 t2 1414 1414 + 1414 = + 9 Evaluate the square roots. = 3 + 1414 18 t2 = 9. = 3 Add. 1414

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( 36) 2

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Your turn Find the two square roots of each number. 1. 81 2. 2500 Evaluate each expression. 3. 3 16 + 1 4. 7 9 – 2 49 9950 13 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

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Squares and Square Roots 4-5

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