TEACHER: SHAROFOV AZIZ
WEEK 12
MATH NOTES
LESSON 6.2 RADICALS AND RATIONAL EXPONENTS (Algebra 1)
OBJECTIVES:
Codes
MA.912
NSO.1.1
Student learning objectives
Find nth roots
Evaluate expression with rational exponents
Solve real life problems involving rational exponents
PREREQUISITES:
Order of Operations (PEMDAS/BODMAS); Properties of Exponents; Addition,
subtraction, multiplication, and division of whole numbers, fractions, and decimals.
KEY WORDS:
Square root; Cubic Root; Annual inflation rate.
CLASS ACTIVITIES: Exercises 1-12, pp. 308-310.
HOMEWORK: Exercises 1,3,5,9,13,21,27,29, p. 318
INTRODUCTION:
Radicals and rational exponents are two interconnected ways of representing roots. Radicals
1
use symbols like √ , while rational exponents express roots as fractions 𝑎 𝑛 . This lesson
explores their relationship, simplifies expressions, and applies exponent rules to solve
problems efficiently.
DEFINITION:
𝒏
The 𝒏𝒕𝒉 roots of 𝒂, denoted as √𝒂, are real numbers that satisfy the following conditions:
𝟏
𝒏
1. If 𝒏 is odd, then 𝒂 has one real 𝒏𝒕𝒉 root: √𝒂 = 𝒂𝒏
𝟏
𝒏
2. If 𝒏 is even and 𝒂 > 𝟎, then 𝒂 has two real 𝒏𝒕𝒉 roots: √𝒂 = ±𝒂𝟐
𝒏
3. If 𝒏 is even and 𝒂 = 𝟎, then 𝒂 has one real 𝒏𝒕𝒉 roots: √𝒂 = 𝟎
4. If 𝒏 is even and 𝒂 < 𝟎, then 𝒂 has no real 𝒏𝒕𝒉 roots.
RATIONAL EXPONENTS:
𝒎
𝒏
𝒎
𝒏
𝒂 𝒏 = √𝒂𝒎 , 𝒐𝒓 𝒂 𝒏 = ( √𝒂)
𝒎
ANNUAL INFLATION RATE:
To calculate the annual inflation rate 𝒓 (in decimal form) of an item increases in value 𝑷
𝟏
𝑭 𝒕
to 𝑭 over a period of 𝒕 years, you can use the equation 𝒓 = (𝑷) − 𝟏.
Exercises: