Name: 9.1 9.1 Radical Expressions and Functions A. Square Root The square root of a number is a value that when ______________________ by _____________ gives the number. For example, ________________________ because ________________________. EX 1: Find the value of the following radical expressions: b. −25 a. 36 c. 1
16
d. −3 64 B. Simplifying Radicals To simplify variables, ________________ the _______________ into the _____________________. That tells you how many of the variables you can _______________________ of the radical sign. EX 1: Simplify the following: 8
b. 81a 6
a. 121b 10 2
2 9x 8 y 4 z12 c. − 16a b d. C. Cube Roots The cube root of a number is a value that when ___________________ by ________________________________ gives the number. For example, ______________________ because _______________________. EX 1: Find the cube root. 3
6
b. −27a 3
3
a. 8b c. 3 −64
125
3
9
d. 4 216x Maya Lanzetta MAT 122 Wherever there is number, there is beauty. ~Proclus D. nth Root Even Index: If you have a __________________ number under the radical sign, you have a ________________________. Odd Index: You ______ have a _________________ number under the radical sign. EX 1: Express without a radical sign: 4
a. 16 E. Radical Functions 5
10
b. −243a EX 1: Given the radical function g(x) = 3 + 3 x find g(2) . Round to the nearest hundredth. EX 2: Many birds drop clams or other shellfish in order to break the shell and get the food inside. The time t (in seconds) it takes for an object such as a clam to fall a certain distance d (in feet) is given by the equation t =
d
. A gull drops a 4
clam from a height of 50 feet. A second gull drops a clam from a height of 32 feet. Find the difference in the times that it takes for the clams to reach the ground. Round to the nearest hundredth. G. Graphing Radical Functions f (x) = x Find Domain and Range: f (x) = x − 4 − 5 Find Domain and Range: Challenge: Which of the following is the smallest? A. 10
10
B. 101 C. 10 D. 1
10
E. 10 110