Powers and Roots• Corresponding to every power there is a root. – Examples: If , then If , then If , then
The nth Root• If , with a and b real numbers and n a positive integer, then a is an nth root of b If n is odd… If n is even… There is one real nth root of b And b is positive, there are two ( + )real nth roots of b. • The positive root is the principle root: • The negative root is its opposite: And b is negative, there are no real nth roots of b.
Vocabulary• You use a radical sign to indicate a root• The number or term under the radical sign is called the radicand• The index gives the degree of the root. n a
Finding all Roots• To find the roots of a number, ask yourself “What raised to the n power, gives the radicand?” – To find the roots of a fraction, consider the numerator and denominator separately – Don’t forget about Positive and Negative numbers
Example: Find all the real roots Find all the real cube roots of each number1. 10002. 0.0083. 1 27
Example: Find all the real roots Find all the real fourth roots of each number1. 12. -0.00013. 16 81
Example: Simplify 3 12 151. a b 8 122. 4 x y 4 12 163. x y
Example (p364)Some teachers adjust test scores when a testis difficult. One teacher’s formula for adjustingscores is A 10 R where A is the adjustedscore and R is the raw score. If the raw scoreson one test range from 36 to 90, what is therange of adjusted scores?