Powers and Exponents, Square Roots Pg. 25 – 28, 52 - 61

Definitions FACTORS – Two or more numbers multiplied together to form a product 5 • 7 = 35 5 and 7 are the factors 35 is the product When the same factor is used, you can use an exponent. 3 • 3 = 9, or 32 = 9 3 is the BASE and 2 is the EXPONENT

Powers Numbers expressed by using exponents are called POWERS. 53 is “ 5 to the third power or 5 cubed. 53 = 5 • 5 • 5 125 34 is “3 raised to the fourth power” 34 = 3 • 3 • 3 • 3 81 42 is “4 raised to the second power or 4 squared” 42 = 4 • 4 16

Write each power as a product of the same factor 62 6 • 6 74 7 • 7 • 7 • 7 26 2 • 2 • 2 • 2 • 2 • 2

More Definitions You can EVALUATE, or find the value of, powers by multiplying the factors. Numbers written without exponents are in STANDARD FORM. Evaluate 63 6 • 6 • 6 36 • 6 216 Numbers written with exponents are in EXPONENTIAL FORM. 9 • 9 • 9 •9 94

Squares and Square Roots The product of a number and itself is the SQUARE of that number. 2 • 2 = 22 = 4 Numbers like 9, 25 and 81 are called PERFECT SQUARES. 32 = 9 52 = 25 92 = 81 The SQUARE ROOT of a number is one of its two equal factors 9 =3 25 =5 81 =9

Estimate square roots Estimate the 60 22 = 4, 32 = 9, 42 = 16, 52 = 25, 62 = 36, 72 = 49, 82 = 64, 92 = 81, 102 = 100 Estimate the 60 60 is not a perfect square. 60 lies between 49 (72) and 64 (82). Since 60 is closest to 64, the best whole number estimate is 8 Estimate the 17 17 is not a perfect square. It lies between 16 (42) and 25 (52). Since 17 is closest to 16, the best whole number estimate is 4. Any number that is not a perfect square has a square root that is an IRRATIONAL NUMBER.