Download 6-2: Multiplying and Dividing Radical Expressions Simplifying Radicals Simplifying Products

6-2: Multiplying and Dividing
Radical Expressions
Algebra 2
Combining Radical Expressions:
Products

If n a and n b are real numbers, then:
n
n
a
b  n ab
index
◦ If the radicals have the same __________,
they can be ____________.
combined
Simplifying Radicals

2
3
5
30
4  3 2  4   3 8  2
3
5 Different index, can’t be combined
Simplifying Products
Reduce the ____________
as much as
radicand
possible.
root
◦ Simplify until all ____
factors are
nth ________
taken.
3
3
32x5 y 6  3 8 4 x x x x x y y y y y y

Combine using multiplication then
simplify
index
◦ Remember the __________
must be the
same.
35 xy 4  9 5 x5 y 3
45 x5 y 3
7 5 xy 4
 9 7 5 5 x5 x y 4 y 3
 3 23 4 x x x x x y y y y y y
 9 7 5 5 x6 y 7
 2 xy 2 3 4 x 2
 3 5 x3 y 3 7 y  15 x3 y 3 7 y
Dividing Radicals

If n a and n b are real
numbers and b≠0,
n
n
18 x
5
2 x3

Rationalizing the
Denominator.
2
2  2



2
2  2 
a na

b
b

What is the simplest form of
5
18 x
2 x3

2 2
2
 9x 2
 3x
 2
3
3
4𝑥 4
?
32𝑦𝑧 3
3
4x4
4 x4

32 yz 3 3 32 yz 3
4 x4
3
4 22 y 2
42 2 yz 3
3
4 22 y 2
3

3

3
4 x 4 4 22 y 2
3
43 23 y 3 z 3
4 x 3 xy 2 x 3 xy 2


8 yz
2 yz
You must find what the radicand in the denominator needs
to make each of its factors a perfect cube.
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Homework: p. 371 #10-50 even
2