1. 7.1 Warm-Up Evaluate the expression: √ √ √ Solve each equation.
2. – √
3. ( ) 2 √ 3
- 11 25
Solve each equation.
4. x² = 49
x = -7, 7

2. 7.1 Roots and Radical Expressions
Objective: To learn how to evaluate nth roots of real numbers
using both radical notation and rational exponent
notation.
State Standard: Students determine whether a specific algebraic statement involving radical expressions is sometimes true, always true, or never true.
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3. 7.1 Roots and Radical Expressionsⁿ √ a
nth root of a:
index: the integer n (greater than 1) is an nth root of a.
2³ = is a cube root of 8
34 = is a fourth root of 81

4. -2 4 Example 1: Find the indicated real nth root(s) of a.
A. n = 5, a = -32
Radical Notation
Exponential Notation 5
-32 √
B. n = 3, a = 64
(-32)
1/5 64 3 √
1/ 3 64 -2 4

5. -3 3 On White Board Find the indicated real nth root(s) of a. -27 √
1. n = 3, a = -27 3
-27 √
2. n = 4, a = 81
(-27)
1/3 81 4 √
1/ 4 81 -3 3

6. 2xy2 -3c2 x2y3 On White Board Simplify 4x2y4 √ 22x2(y2)2 √ -27c6 √1. 2.
22x2(y2)2 √
-27c6 3 √
(-3)3(c2)3 3 √ 3.
x8y12 4 √
2xy2
(x2)4(y3)4 4 √
-3c2
x2y3

7. Let a be an nth root of a, and let m be a positive integer.
RATIONAL EXPONENTS
Let a be an nth root of a, and let m be a positive integer.
1/n
a = (a ) = ( a )
m/n
1/n m n √
a = = , a = 0
a (a )
-m/n
m/n
1/n m
Example 2
a = ( 16) = 4 =
5/2 5 √
1024
16 = (16 ) = 4 =
5/2
1/2 5
1024

8. 7.1 Guided Practice
Page 378
5, 9, 13 – 23 odd

9. 7.1 HOMEWORK
Page 378
5, 9, 13 – 23 odd, 26 – 28, 43 – 49