SECTION
9.1: RADICALS, INDEXES, RADICANDS
The following symbol, , is called a "radical" symbol or a "root" symbol. In general, you'll see a number inside this little "v" portion of the
radical (root) symbol. That number inside the v portion of the radical (root)
symbol is called an "index." The math expression "inside" the
radical symbol is called the "radicand."
A radical with an index of 2, is called a "square root." In general, math people do not place a 2 in the
index position: if you see it is understood to be a "square root." A radical with an
index of 3, is called a "cube root." A radical with an index of 4, is called a "fourth root." A radical with an index of n, is called a "nth root."
EXAMPLES OF ROOTS 

pronounced "square root of 2" 

pronounced "cube root of 5" 

pronounced "fourth root of 9" 

pronounced "fifth root of 7" 

pronounced "seventeenth root of 9234" 
SECTION 9.2: TWO INDEX RULES
OF RADICALS
ROOTS WITH INDEXES THAT ARE POSITIVE EVEN INTEGERS 
If "a" is a positive even integer and "b" is a positive real
number
then means
"What positive real number raised to the power of "a" will result in
"b"?" 
ex. 1) √ 4 is asking "What positive real number raised to the power of 2 will result in 4?"
The answer is 2.
Why? Because 2^{2} = 4. Hence, we say √ 4 = 2.
Comment: Rememeber if there is no index in the root, the root is assumed to have an index of 2.
ex. 2) is asking "What positive real number raised to the power of 4 will result in 81?"
The answer is 3.
Why? Because 3^{4} = 81. Hence, we say = 3.
ex. 3) is asking "What positive real number raised to the power of 6 will result in 64?"
The answer is 2.
Why? Because 2^{6} = 64. Hence, we say = 2.

ROOTS WITH INDEXES THAT ARE POSITIVE ODD INTEGERS 
If "a" is a positive odd integer and "b" is any real number
then means
"What real number raised to the power of "a" will result in
"b"?"
Comment: In this case your answer will be positive or
negative depending on the radicand. 

ex. 1) is asking "What real number raised to the power of 3 will result in 8?"
The answer is 2.
Why? Because 2^{3} = 8. Hence, we say = 2.
ex. 2) is asking "What real number raised to the power of 5 will result in 32?"
The answer is 2.
Why? Because (2)^{5} = 32. Hence, we say = 2.
Comment: Roots with odd indexes can have radicands that are negative and answers that are negative. 
SECTION 9.3: ROOTS AS EXPONENTS
There is rule that allows you to transform a radical into an exponential. It
is as follows:
RADICAL TO EXPONENT RULE 

ex. 1) can be rewritten as 8^{ 1/3}.
ex. 2) can be rewritten as (32)^{ 1/5}.
ex. 3) can be rewritten as (81)^{ 1/4}.
ex. 4) can be rewritten as (32)^{ 1/6}. 



THE SUMMER STUDY GUIDE
BY CHAPTERS

RETURN TO THE SUMMER STUDY GUIDE MAIN PAGE
 CHAPTER 1: THE NUMBER SYSTEM
 CHAPTER 2: ORDER OF OPERATIONS
 CHAPTER 3: VARIABLES, MONOMIALS,
BINOMIALS, TRINOMIALS, POLYNOMIALS,
COEFFICIENTS, TERMS AND LIKE TERMS
 CHAPTER 4: SIGNED NUMBERS,
ABSOLUTE VALUE, AND INEQUALITY SYMBOLS
 CHAPTER 5: FACTORS, COMMON
FACTORS, LEAST COMMON FACTORS AND GREATEST COMMON FACTORS
 CHAPTER 6: PROPERTIES OF NUMBERS
 CHAPTER 7: THE WORLD OF FRACTIONS
 CHAPTER 8: EXPONENTS
 CHAPTER 9: ROOTS
 CHAPTER 10: ALGEBRAIC EXPRESSIONS
 CHAPTER 11: CARTESIAN COORDINATE SYSTEM
 CHAPTER 12: SETS, RELATIONS AND FUNCTIONS
 CHAPTER 13: AVERAGE RATE OF CHANGE OF Y WITH RESPECT TO X, SLOPE, PYTHAGOREAN THEOREM, AND DISTANCE FORMULA BETWEEN TWO POINTS
 CHAPTER 14: XINTERCEPT(ZERO) AND Y INTERCEPT(B)
 CHAPTER 15: LINES
 CHAPTER 16: FUNCTIONS
 CHAPTER 17: MULTIPLYING POLYNOMIALS
 CHAPTER 18: FACTORING
 CHAPTER 19: RATIONAL EXPRESSIONS
 CHAPTER 20: SOLVING EQUATIONS
 CHAPTER 21:SOLVING INEQUALITIES
 CHAPTER 22: SOLVING A SYSTEM OF EQUATIONS
 CHAPTER 23: QUADRATICS
 CHAPTER 24: CIRCLES
 CHAPTER 25: AREAS AND PERIMETERS OF PLANE FIGURES
 CHAPTER 26: VOLUMES
