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Unit 2 Notes Day 5 EQ: How do I determine what numbers are perfect squares?

Unit 2 Notes Day 5 EQ: How do I determine what numbers are perfect squares?. By definition Ö 25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that Ö 25 = 5.

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Unit 2 Notes Day 5 EQ: How do I determine what numbers are perfect squares?

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  1. Unit 2 Notes Day 5 EQ: How do I determine what numbers are perfect squares?

  2. By definition Ö25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that Ö25 = 5 Numbers like 25, which have whole numbers for their square roots, are called perfect squares You need to memorize at least the first 25 perfect squares

  3. Square root Square root Perfect square Perfect square 1 81 Ö1 = 1 Ö81 = 9 4 100 Ö4 = 2 Ö100 = 10 9 121 Ö9 = 3 Ö121 = 11 16 144 Ö16 = 4 Ö144 = 12 25 169 Ö25 = 5 Ö169 = 13 36 196 Ö36 = 6 Ö196 = 14 49 225 Ö49 = 7 Ö225 = 15 64 Ö64 = 8

  4. Square root Square root Perfect square Perfect square 256 576 Ö256 = 16 Ö576 = 24 289 625 Ö289= 17 Ö625= 25 324 Ö324= 18 361 Ö361= 19 Ö400= 20 400 441 Ö441= 21 484 Ö484 = 22 529 Ö529 = 23

  5. Every whole number has a square root Most numbers are not perfect squares, and so their square roots are not whole numbers. Most numbers that are not perfect squares have square roots that are irrational numbers Irrational numbers can be represented by decimals that do not terminate and do not repeat The decimal approximations of whole numbers can be determined using a calculator

  6. When you press the key on a calculator, only the nonnegative square root appears. This is called the principal square root of the number. 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.

  7. 49 = 7 225 = 15 49 = –7 225 = –15 100 = 10 100 = –10 Find the two square roots of each number. A. 49 7 is a square root, since 7 • 7 = 49. –7 is also a square root, since –7 • –7 = 49. B. 100 10 is a square root, since 10 • 10 = 100. –10 is also a square root, since –10 • –10 = 100. C. 225 15 is a square root, since 15 • 15 = 225. –15 is also a square root, since –15 • –15 = 225.

  8. 25 = 5 289 = 17 25 = –5 289 = –17 144 = 12 144 = –12 Find the two square roots of each number. E. 25 5 is a square root, since 5 • 5 = 25. –5 is also a square root, since –5 • –5 = 25. F. 144 12 is a square root, since 12 • 12 = 144. –12 is also a square root, since –12 • –12 = 144. G. 289 17 is a square root, since 17 • 17 = 289. –17 is also a square root, since –17 • –17 = 289.

  9. So 169 = 13. Remember! The area of a square is s2, where s is the length of a side. H. A square window has an area of 169 square inches. How wide is the window? Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning. 132 = 169 The window is 13 inches wide.

  10. 16 = 4 I. 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? Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning. So the table is 4 feet wide, which is less than 5 feet, so it will fit through the van door.

  11. Obj: To find the square root of a number • Find the square roots of the given numbers • If the number is not a perfect square, find the two numbers that the square root is between. 81 Ö81 = 9 37 Ö37 is between 6 and 7 158 Ö158 is between 12 and 13

  12. Obj: To find the square root of a number • Find two consecutive whole numbers that the given square root is between • Try to do this without using the table Ö16 = 4 and Ö25 = 5 so Ö18 Ö18 is between 4 and 5 Ö115 Ö100 = 10 and Ö121 = 11 so Ö115 is between 10 and 11

  13. Multiplying radicals The product of the square roots of two numbers is the same as the square root of the product of the numbers Examples: Ö3 · = Ö12 Ö36 Ö7 · = Ö11 Ö77

  14. Simplify the following expressions -Ö4 = -2 = 7 8 + 9 · 7Ö64 + 9 = 56 + 9 = 65 5 + = 5 5 + 7 · Ö25 Ö49 = 25 + 7 = 32

  15. Simplify the following expressions Ö 4 Ö4 2 = = 81 Ö81 9 1 1 Ö 1 Ö 1 – – = 12 6 36 144 1 2 – = 12 12 1 = 12

  16. Simplified radical form No factor inside the radical should be a perfect square. Ö18 = = Ö2 = 3 Ö2 Ö9 2 Ö9 · Ö108 = = Ö3 = 6 Ö3 Ö36 3 Ö36 · Ö96 = = Ö6 = 4 Ö6 Ö16 6 Ö16 ·

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