Martin-Gay, Developmental Mathematics 1 Warm-Up #8 (Monday, 9/21)

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