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Martin-Gay, Developmental Mathematics 1
Warm-Up #8 (Monday, 9/21)
1.
Martin-Gay, Developmental Mathematics 2
Homework (Monday 9/21)
Rationalize the denominators worksheet
Advanced: front #1-10 ALL, back #1-2
Regular: front #1-8 ALL, back #1
Multiplying and Dividing Radicals
Martin-Gay, Developmental Mathematics 4
nnn abba
0 if b b
a
b
an
n
n
n a n bIf and are real numbers,
Multiplying and Dividing Radical Expressions
Martin-Gay, Developmental Mathematics 5
Simplify the following radical expressions.
xy 53 xy15
23
67
ba
ba
23
67
ba
ba44ba 22ba
Multiplying and Dividing Radical Expressions
Example
Martin-Gay, Developmental Mathematics 6
If we rewrite the expression so that there is no radical in the denominator, it is called rationalizing the denominator.
Rationalizing the denominator is the process of eliminating the radical in the denominator.
Rationalizing the Denominator
Martin-Gay, Developmental Mathematics 7
Rationalize the denominator.
2
3
2
2
3 9
6
3
3
3
3
22
23
2
6
33
3
39
3 6
3
3
27
3 6
3
3 6 33 3 2
Rationalizing the Denominator
Example
Martin-Gay, Developmental Mathematics 8
Martin-Gay, Developmental Mathematics 9
2 5
2 1
22 5
2 11
1
2
4 2 5 2 5
4 2 2 1
2 6 2 5
2 1
7 6 2
1
7 6 2
If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required.
conjugate
Martin-Gay, Developmental Mathematics 10
3
2 7
7
2 77
2
2
3
6 3 7
4 2 7 2 7 49
6 3 7
4 7
6 3 7
3
3 2 7
3
2 7 2 7
conjugate
Martin-Gay, Developmental Mathematics 11
Many rational quotients have a sum or difference of terms in a denominator, rather than a single radical.
•need to multiply by the conjugate of the denominator
•The conjugate uses the same terms, but the opposite operation (+ or ).
Conjugates
32
23
15
23
Martin-Gay, Developmental Mathematics 12
Martin-Gay, Developmental Mathematics 13
Rationalize the denominator.
32
23
332322
3222323
32
32
32
322236
1
322236
322236
Rationalizing the Denominator
Example
Martin-Gay, Developmental Mathematics 14