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Warm Up #2
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HW Check – Exponents Practice
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7.1
Simplifying Radical Expressions
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Nth Root
For any real number a and b, and any
positive integer n, if an = b , then a is the
nth root of b.
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Real Number Examples:
Find the roots:
1.
Square Root of 4
Square Root of -4
2.
Cube Root of 8
Cube Root of -8
Even Index, Negative Radican = No Real Solution
Odd Index, Negative Radican = Negative Solution
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Simplifying Radical Numbers
- Find the largest perfect square/cube factor.
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Take the square/cube of the factor, goes on the
outside
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Leftover factor stays INSIDE the radical.
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Variable Examples:
For variables you take GROUPS of the
index out, leaving the remainder in!
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Warm Up
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Section 7.2
Multiplying &
Dividing Radicals
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Multiplying Radical
Expressions
 If
they are real numbers, then
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Examples:
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Dividing Radical Expressions
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Examples:
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Rationalizing the Denominator
**Multiply the numerator and denominator
by the denominator**
Then Simplify
Example: 1.
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2.
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Warm Up #3
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HW Check – 7.2 Odds
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7.3
Adding, Subtracting, Multiplying and Dividing
Binomial Radical Expressions
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Adding Radical Expressions
 Use
the same concept as that of adding or
subtracting like variables.
 Example:
7 - 3x + 2x + 5
*Have to have like Terms to Add/Subtract*
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Like Radicals are radical expressions that
have the same index and the same
radicand.
3 x 2 x 
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Like Radicals
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Unlike Radicals
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Examples:
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2.
4 26 2 
7 52 52 4 
+3.
4.
8 x 2 x 
6 27 2
5.
5 78 7 
6.
3 63 5 5
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Always simplify radicals before
combining!
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Multiplying Binomials
To multiply, USE FOIL!
Example 1:
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2.
3.
( 1  3)( 1  3)
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Dividing Binomial Radicals
To divide, Rationalize the denominator!
(a + b)( a - b) = a2 – b2
These are called conjugates! They make
radicals disappear!
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Examples:
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2.
8
6- 3
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Examples:
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7.4 Rational Exponents
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Rational Exponents
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Rational Exponents are another way to write radicals.
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Simplify each expression.
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Rational Exponents to Radicals
The
Denominator is the INDEX
The
Numerator is the POWER
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Converting to Radical Form
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Converting to Exponential Form
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Properties of Exponents also apply to Rational Exponents!
Write in Radical Form:
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Simplify each expression.
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Warm Up #4
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HW Check – 7.4
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7.5 Solving Radical Equations
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Radical Equations
A radical equation is an equation
that has a variable in a radicand or
has a variable with a rational
exponent.
Are these Radical Equations?
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We use inverse operations to solve
equations.
Solve:
X2 = 4
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What is the inverse of cubing x?
Solve:
X3 = 64
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Solve the following. Check your
solutions!
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2.
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6.
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**To solve radical equations
with rational exponents, raise
each side to the reciprocal
exponent!
Solve
(x)1/2 = 3
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Examples:
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Solve
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You can also solve by graphing!
Given:
The equation is already equal to zero!
y=
Find the x-intercept!