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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
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Study Strategy –Note Taking

•Choosing a Seat
•Note-Taking Speed
•Things to Include
•Being an Active Learner
•Write Down Each Step

Section 8.1–Square Roots and Radical Notation

The principal square root of b, denoted ,
is the positive number a such that a2 =b
The expression is called a radical
expression.

The sign is called a radical sign.
The expression contained inside the

Simplify:  because 72 =49

Simplify, assume x is nonnegative: . because For any index n>1and any nonnegative
numbers a and b, Simplify:  Simplify:  For any index n>1and any nonnegative
number a and positive number b , Simplify:  2. Rewrite each factor as a product of two
factors. The exponent for the first factor should
be the largest multiple of the radical’s index that
is less than or equal to the factor’s original
exponent.
3. Use the product property to remove factors

Simplify:  Two radical expressions are called like
radicals if they have the same index and the factors in front of the radicals.

Subtract:  Add:  Section 8.3 –Multiplying and Dividing Radical Expressions

If the index of each radical is the same,
multiply factors in front of the radical by
each other, and multiply the radicands by
each other. Simplify the resulting radical if
possible.

Multiply:  If one or more of the expressions contains at
least two terms, multiply by using the
distributive property.

Multiply:  Multiply:  To square a radical expression containing two or more terms, multiply the expression by itself.

Multiply:  Concept –Rationalizing a Denominator with Only
One Term Containing a Radical with an Index of n

1. Multiply both the numerator and denominator
by a radical expression that results in the
radicand being a perfect nth power.
2. Simplify the radical in the denominator.
3. Simplify the fraction by dividing out factors
that are common to the numerator and
denominator, if possible.

Example -Rationalizing a Denominator with Only
One Term Containing a Radical with an Index of n

Rationalize the denominator:  