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Name: ____________________________ Period: ______ Date: ____________ Algebra II
Notes for 6.2,6.3: Multiplying and Dividing Radical Expressions. Binomial Radical Expressions.
Take a note:
You can simplify the product of powers that have the same exponent. Similarly, you can simplify the
product of radicals that have the same index You can. You can simplify a radical expression when the
exponent of one factor of the radicand is a multiple of the radical’s index.
Example:
n
n
n
n
Property : If
a and b are real numbers  n a  b  ab
Problem 1: Multiplying Radical Expressions.
Can you simplify the product of the radical expressions? Explain.
A. 3 6  2 
B.3 - 4  3 2 
Your turn: Can you simplify the product of the radical expressions? Explain.
a )4 7  5 7 
b )5  5  5  2 
Note: If the radicand has a perfect nth power among its factors, you can reduce the radical. If you
reduce a radical as much as possible, the radical is in the simplest form.
Problem 2: Simplifying a radical Expression
What is the simplest form 3 54 x 5 ?
Problem 3: Simplifiying a Product
What is the simplest form of
72 x 3 y 2  10 xy 3 ?
Your turn: What is the simplest form of
3
128x 7 ?
Your turn: What is the simplest 45x 5 y 3  35xy 4 ?
Property: If n a and n b are real numbers and b  0, then
n
a
n
b
n
a
b
Problem 4: Dividing Radical Expressions
What is the simplest form of the quotient?
A.
18 x 5
162 y 5
3
B.
2x 3
3
Your turn: What is the simplest form of
50x 6
2x 4
3y 2
?
Note: Another way to simplify an expression is to rationalize the denominator. You rewrite the
expression so that there are no radicals in any denominator and no denominator in any radical.
Problem 5: Rationalizing the Denominator
What is the simplest form of
Your turn:
3
5x 2
12 y 2 z
3
What is the simplest form of
3
7x
5y 2
?
Take a note: Like radicals are radical expressions that have the same index and radicand.
When multiplying binomial radicals expressions use FOIL.
Property: Combining Radicals Expressions : Sums and Difference
Use he Distributive Property to add or subtract like radicals
a n x  bn x  a  b n x
a n x  bn x  a  b n x
Problem 6: Adding and Subtracting Radical Expressions
What is the simplified form of each expression?
a )3 5 x  2 5 x 
b)6 x 2 7  4 x 5 
c )123 7 xy  85 7 xy 
Your turn: What is the simplified form of each expression?
a )73 5  4 5
b)3 x xy  4 x xy
c)175 3x 2  155 3 x 2
Your turn again: Using radical expression
1.)This tile design is made of congruent right triangles with base 1 ft and height 2 ft. Find the perimeter
of the tile to the nearest tenth of a foot.
2.) What is the simplest form of the expression?(remember to simplified before adding or subtracting)
a) 12  75  3 
b)3 250  3 54  3 16 
Problem 7: Multiplying Binomial Radical Expressions
What is the product of each radical expression?



a) 4  2 2 5  4 2 






b) 3  7 5  7 
c) 5  7 5  7 
Your turn: What is the product of each radical expression



b)6  12 6  12  
c)3  8 3  8  
a) 3  2 5 2  4 5 
Problem 8: Rationalizing the denominator
Take a note: Conjugate are expressions that only differ in the signs of the second term
How can you write the expression with a rationalized denominator?
3 2
5 2
Your turn: How can you write the expression with a rationalized denominator
a)
b)
2 7
3 5
4x
3 6