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Chapter4.6

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Chapter4.6

1. 1. Warm Up California Standards Lesson Presentation Preview
2. 2. Warm Up Simplify. 25 64 144 225 400 1. 5 2 2. 8 2 3. 12 2 4. 15 2 5. 20 2
3. 3. NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not a square, determine without a calculator the two integers between which its square root lies and explain why. Also covered: AF2.2 California Standards
4. 4. Vocabulary square root principal square root perfect square
5. 5. The square root of a number is one of the two equal factors of that number. Squaring a nonnegative number and finding the square root of that number are inverse operations. Because the area of a square can be expressed using an exponent of 2, a number with an exponent of 2 is said to be squared . You read 3 2 as “three squared.” 3 3 Area = 3 2
6. 6. Positive real numbers have two square roots, one positive and one negative. The positive square root, or principle square root , is represented by . The negative square root is represented by – .
7. 7. A perfect square is a number whose square roots are integers. Some examples of perfect squares are shown in the table.
8. 8. You can write the square roots of 16 as ±4, which is read as “ plus or minus four.” Writing Math
9. 9. Additional Example: 1 Finding the Positive and Negative Square Roots of a Number Find the two square roots of each number. 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. A. 49 B. 100 The square roots of 49 are ±7. The square roots of 100 are ±10. 49 = –7 – 49 = 7 100 = 10 100 = –10 –
10. 10. A. 25 Check It Out! Example 1 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. Find the two square roots of each number. B. 144 The square roots of 144 are ±12. The square roots of 25 are ±5. 25 = –5 – 25 = 5 144 = 12 144 = –12 –
11. 11. 13 2 = 169 The window is 13 inches wide. Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning. Additional Example 2: Application A square window has an area of 169 square inches. How wide is the window? So 169 = 13.
12. 12. Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning. Check It Out! Example 2 A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening? So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door. 16 = 4
13. 13. Additional Example 3: Finding the Square Root of a Monomial Simplify the expression. A. Write the monomial as a square. Use the absolute-value symbol. = 12| c | 144 c 2 B. z 6 = | z 3 | Write the monomial as a square: z 6 = (z 3 ) 2 Use the absolute-value symbol. 144 c 2 = (12 c ) 2 z 6 = ( z 3 ) 2
14. 14. Additional Example 3: Finding the Square Root of a Monomial Simplify the expression. C. Write the monomial as a square. 10n 2 is nonnegative for all values of n. The absolute-value symbol is not needed. = 10 n 2 100 n 4 100 n 4 = (10 n 2 ) 2
15. 15. Check It Out! Example 3 Simplify the expression. A. Write the monomial as a square. Use the absolute-value symbol. = 11| r | 121 r 2 B. p 8 = | p 4 | Write the monomial as a square: p 8 = (p 4 ) 2 Use the absolute-value symbol. 121 r 2 = (11 r ) 2 p 8 = ( p 4 ) 2
16. 16. Check It Out! Example 3 Simplify the expression. C. Write the monomial as a square. 9m 2 is nonnegative for all values of m. The absolute-value symbol is not needed. = 9 m 2 81 m 4 81 m 4 = (9 m 2 ) 2
17. 17. Lesson Quiz  12  50 7| p 3 | z 4 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 Find the two square roots of each number. 1. 144 2. 2500 Simplify each expression. 3. 49 p 6 4. z 8