Download Algebra II/Trig Honors Unit 3 Day 1: Evaluate nth Roots and Use

Algebra II/Trig Honors
Unit 3 Day 1: Evaluate nth Roots and Use Rational Exponents
Objective: To evaluate roots (square roots, cube roots, fourth roots, etc.) and use rational exponents
Terms:

nth root of _________________ is ______, where n is an integer greater than 1.
o the nth root of a is written as: _________________ where n is called the index.
You can also write the nth root of a as a power of a.

a 

a 

a 
12 2
13 3
14 4



Example 1: Find nth roots
Find the indicated nth root(s) of a.
a. n  3 , a  216
b. n  4 , a  81
Rational Exponents (fractional exponents) - _______________________________________
____________________________________________________________________________
Properties of Rational Exponents
1
Let a n be an nth root of a, and let m be a positive integer.
a


a
m
n

m
n


Numerator stands for the ________________. Denominator stands for the ______________.
**Remember: ______________________________
Example 2: Evaluate expressions with rational exponents
Evaluate.
a. 16
3
2
b. 32 3 5
Example 3: Approximate roots with a calculator
3
a. 91 5
b. 12 8
c.
 7
4
3
Example 4: Solve equations using nth roots
Solve the equation.
a. 4 x 5  128
b. x  3  21
4
Note: When n is
even and a > 0, be
sure to use a 
when solving.
Example 5: Use nth roots in problem solving
A study determined that the weight w (in grams) of coral cod near Palawan Island, Philippines, can be
approximated using the model w  0.0167l 3 where l is the coral cod’s length (in centimeters). Estimate
the length of a coral cod that weighs 200 grams.
HW: Page 169 #3-60 (M3), 61