1. Unit 3: Algebra: Rational Exponents and Square Root Functions
3.1 – Evaluate nth Roots and Use Rational Exponents

2. Georgia Performance Standards
MM3A2a
Define and understand the properties of nth roots
MM3A2b
Extend properties of exponents to include rational exponents
MM3A3d
Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology

3. Vocabulary
For an integer n greater than 1, if bn = a, then b is an nth root of a.
An nth root of a is written as 𝑛 𝑎 where n is the index of the radical. If n is odd, then a has one real root. If n is even, then a has two real nth roots if a > 0, one real nth root if a = 0, and no real nth roots if a < 0.

4. Radicals and rational exponents
How can you write the root of an integer using an exponent? An nth root of x is written as 𝑛 𝑥 where n is the index of the radical.
𝑛 𝑥
Index
Radicand

5. Radial Review – Think trees

6. Radial Review

7. Radial Review
Solve the Following: 30
100𝑥3
200

8. Radial Review Solve the Following: 𝟐 * 𝟖 𝟓 * 𝟕 2 𝟐 * 3 𝟓𝟎 𝟑 𝟐 * 𝟑 𝟒
𝟐 * 𝟖
𝟓 * 𝟕
2 𝟐 * 3 𝟓𝟎
𝟑 𝟐 * 𝟑 𝟒
Solve the Following:.
𝟓𝟏𝟐𝐦𝟑
𝟏𝟒𝟕𝐦𝟑𝐧𝟑
-4 𝟏𝟗𝟐𝐱
-3 𝟐𝟒𝐚𝟒𝐛𝟐𝐜𝟑

9. Evaluate (a) 95/2 and (b) 27-2/3
Rational Exponent Form
95/2 = (91/2)5 = 35 = 243
27-2/3 = /3 = 1 (27 1/3 )2 = = 1 9

10. Evaluate (a) 95/2 and (b) 27-2/3
Radical Form
95/2 = ( 9 )5 = 35 = 243
27-2/3 = = = 1 9

11. Using a calculator
Calculator Steps:

12. Solve equations using nth roots
Solve the equation:
-2x6 = -1458
(x+2)5 = 35

13. Solve equations using nth roots
Solve the equation. Round the result to two decimal places:
x = 132
2x = 53
(x+3)4 = 362

14. Try the following
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