unit: radical functions 7-2: multiplying and dividing radical expressions
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Unit: Radical Functions 7-2: Multiplying and Dividing Radical Expressions. Essential Question: I put my root beer in a square cup… now it’s just beer. 7-2: Multiplying and Dividing Radical Expressions. - PowerPoint PPT PresentationTRANSCRIPT
UNIT: RADICAL FUNCTIONS7-2: MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS
Essential Question: I put my root beer in a square cup… now it’s just beer.
7-2: Multiplying and Dividing Radical Expressions
If two terms share the same type of radical, the numbers underneath can be multiplied together.
2 8
2 8
16
4
3 3
3
3
5 25
5 25
125
5
2 8
2 8
16
not possible
7-2: Multiplying and Dividing Radical Expressions
YOUR TURN: Multiply. Simplify, if possible.
3 12 3 33 9 4 44 4
3 12
36
6
3
3
3 9
27
3
4
4
4 4
16
not possible
7-2: Multiplying and Dividing Radical Expressions
Simplifying Radical Expressions (radicals that contain variables) works the same way as simplifying square roots.
Alternately: Use factor trees to simplify numbers underneath roots and the rules of exponent division to simplify variables underneath roots.
3
3
26 6
72
72
2
6 2
6 2
x
x
x x
x x
x x
3 5
3 53
3 233
3 23
3 2
80
80
2 5
2 10
2 1
2
0
2 2
n
n
n n
n n
n n
7-2: Multiplying and Dividing Radical Expressions
YOUR TURN: Simplify. Assume all variables are positive.
450x 3 418x4
4
2
50
50
2
5 2
5
5 5
2
x
x
x
x x
x
x
x x
3 43
333
3 3
3
18
2 3 3
18
18
x
x x
x x
x x
7-2: Multiplying and Dividing Radical Expressions
To multiply radical expressions, multiply terms underneath the radical, then simplify
2 3 3 43 3
5 73
3 5 73 3
3 3 2 3 33 3 3
3 2 23 3
2 23
54 5
270
270
3 10
3 10
3 10
x y x y
x y
x y
x x y y y
x x y y
xy x y
7-2: Multiplying and Dividing Radical Expressions
YOUR TURN Multiply and simplify. Assume all variables
are positive.
3 3 23 7 2 21x x y6 26 147x y
6 26 147 x y 6 26 49 3 x y
36 7 3 x y 342 3x y
7-2: Multiplying and Dividing Radical Expressions
Assignment Page 377 1 – 22 (all problems)
UNIT: RADICAL FUNCTIONS7-2: MULTIPLYING AND DIVIDING RADICAL EXPRESSIONS (DAY 2)
Essential Question: Describe how to multiply and divide two nth roots, both of which are real numbers.
7-2: Multiplying and Dividing Radical Expressions
Dividing has the same limitations as multiplying: if two terms share the same type of radical, they can be combined and then simplified.
3
33
3
32 32
44
8
2
3 5 5
323 2
3 33 33
3
3
3 3
162 162
33
54 2
3 2
3 2
3
x x
xx
x x
x
x
7-2: Multiplying and Dividing Radical Expressions
YOUR TURN: Divide and simplify. Assume all variables
are positive.
243
27
243
27
9
3
412
3
x
x
4
3
3
12
3
4
4
2
x
x
x
x
x x
154
4
1024
4
x
x
15
4
144
1444
3 24
1024
4
256
256
4
x
x
x
x
x x
7-2: Multiplying and Dividing Radical Expressions
Rationalizing the Denominator Rationalizing means to rewrite a problem so
there are no root symbols in the denominator of a fraction.
After dividing (if possible), multiply the numerator and denominator by whatever root remains on the denominator.
Examples using square roots:
3
2
3
2
33 3
6
3
22
5
5 5
5 55
5
5
y
y
x
xy
x y x yx
y yy
7-2: Multiplying and Dividing Radical Expressions
YOUR TURN: Rationalize the denominator.
5
5
7 35
55
7
5
35
10
x y
xy
2 22 2
2 22
2
2
x x x
2
2
x
7-2: Multiplying and Dividing Radical Expressions
Rationalizing the Denominator Rationalizing means to rewrite a problem
so there are no root symbols in the denominator of a fraction.
Example using a cube root:
3 2 2
3
3
3
3 23
3 2 2
3
3
2
3
2 18
33
x
x
xx
x
x
7-2: Multiplying and Dividing Radical Expressions
YOUR TURN: Rationalize the denominator.
3
33
5 5
4 4y y
2 23
2 2
23 3
3 3
805
44
4
4 y
y
y
y
y
22 2 233 3 38 1080 2 10 10
4 4 4 2
yy y y
y y y y
7-2: Multiplying and Dividing Radical Expressions
Assignment Page 377 23 – 34 (all problems)