1. WARM UP Evaluate without using a calculator. 1. √121 2. 5–2
1. √121
2. 5–2
Evaluate without using a calculator.
3. Solve (x + 7)2 = 24. Write answers with radicals in
simplest form.

2. Rational Exponents and nth roots
EQ: What is the relationship between nth roots and rational exponents?
Assessment: Students will write a summary about the relationship between nth roots and rational exponents.

3. Key Terms
nth root of a – __________________________________________________________________________
Index of a radical – __________________________________________________________________________
For an integer n greater than 1, if bn = a,
then 𝒏 𝒂 =𝒃 the nth root of a is equal to b
An nth root of a is written as 𝒏 𝒂 , where n is the index of a radical.

4. Key Concept

5. Example 1 Find the indicated real nth root(s) of a. a. n = 3, a = –216
b. n = 4, a = 81

6. Key Concept

7. Example 2 Evaluate (a) 163/2 and (b) 32–3/5. Rational Exponent Form
Radical Form

8. Example 3 Approximate roots with a calculator a. 91/5 9 1 5
Expression
Keystrokes
Display
a /5
b /8 7
c. ( )3 = 73/4 

9. Example 4
Solve the equation.
a. 4x5
= 128
b. (x – 3)4
= 21

10. You Try It! Find the indicated real nth root(s) of a. 1. n = 6, a = 64
Evaluate expressions without using a calculator.
2. 45/2
3. 9–1/2
Solve the equation. 4.
3x2 = 108 5.
( x + 5 )4 = 16

11. HOMEWORK Textbook – Pg. 417-418 15,19, 24,25,27,31,33,51-53
Write your Summary to the Essential Question
What is the relationship between nth roots and rational exponents?