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Akar dan Radikal (Square Roots and Radical)

Akar dan Radikal (Square Roots and Radical). Because we are familiar with multiplication, we know that Ö 25 = 5. Numbers like 25, which have whole numbers for their square roots, are called perfect squares. You need to memorize at least the first 15 perfect squares. Square root.

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Akar dan Radikal (Square Roots and Radical)

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  1. Akar dan Radikal (Square Roots and Radical)

  2. 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 15 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. 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

  5. Obj: Estimating 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

  6. A. 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

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

  8. 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

  9. B. 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 ·

  10. Just in case you forgot.. The Real Number Line is next..

  11. Graphing real numbers The graph of a number is a dot placed where the number would be on the number line 12 Graph the number: 3 -10 -5 0 5 10 Graph the number: -8.5 -10 -5 0 5 10

  12. HAL-HAL PENTING • Mengalikan Akar • Menyederhanakan Bentuk Akar • Merasionalisasikan Pecahan Akar • Akar ke-n.

  13. A. 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. B. 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 ·

  15. C. Rationalizing Improper Fractions • Multiply the fractions with its corresponding “Akar Sekawan” D. Akar ke-n

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