Akar dan Radikal Square Roots and Radical Because

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 Perfect square 1 Ö 1 = 1 81 4 Ö 4 = 2 100 Ö 100 = 10 9 Ö 9 = 3 121 Ö 121 = 11 16 Ö 16 = 4 144 Ö 144 = 12 25 Ö 25 = 5 169 Ö 169 = 13 36 Ö 36 = 6 196 Ö 196 = 14 49 Ö 49 = 7 225 Ö 225 = 15 64 Ö 64 = 8 Perfect square Square root Ö 81 = 9

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

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 Ö 18 Ö 16 = 4 and Ö 25 = 5 so Ö 18 is between 4 and 5 Ö 115 Ö 100 = 10 and Ö 121 = 11 so Ö 115 is between 10 and 11

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: Ö 3 · Ö 12 = Ö 36 Ö 7 · Ö 11 = Ö 77

Simplify the following expressions -Ö 4 = -2 7Ö 64 + 9 = 7 · 8 + 9 = 56 + 9 = 65 5Ö 25 + Ö 49 = 5 · 5 + 7 = 25 + 7 = 32

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

B. Simplified radical form No factor inside the radical should be a perfect square. Ö 18 = Ö 9 · 2 = Ö 9 Ö 2 = 3 Ö 2 Ö 108 = Ö 36 · 3 = Ö 36 Ö 3 = 6 Ö 3 Ö 96 = Ö 16 · 6 = Ö 16 Ö 6 = 4 Ö 6

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

Graphing real numbers The graph of a number is a dot placed where the number would be on the number line Graph the number: -10 -5 1 32 0 5 10 Graph the number: -8. 5 -10 -5 0

HAL-HAL PENTING A. B. C. D. Mengalikan Akar Menyederhanakan Bentuk Akar Merasionalisasikan Pecahan Akar ke-n.

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: Ö 3 · Ö 12 = Ö 36 Ö 7 · Ö 11 = Ö 77

B. Simplified radical form No factor inside the radical should be a perfect square. Ö 18 = Ö 9 · 2 = Ö 9 Ö 2 = 3 Ö 2 Ö 108 = Ö 36 · 3 = Ö 36 Ö 3 = 6 Ö 3 Ö 96 = Ö 16 · 6 = Ö 16 Ö 6 = 4 Ö 6

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