SWBAT…simplify radicals using the product property of radicals Wed, 3/14

Agenda 1. WU (10 min)2. Lesson on product property of radicals – 13 examples! (30 min)

Warm-Up:

HW #6: Simplifying radicals

Simplifying Radical Expressions

Properties of Radicals

ab a b

ab

a

b

aaa

1n na a

In the expression , is the radical sign and 64 is the radicand.

64

1 • 1 = 12 • 2 = 43 • 3 = 9

4 • 4 = 165 • 5 = 256 • 6 = 36

49, 64, 81, 100, 121, 144, ...

What numbers are perfect squares?

Product Property of Radicals

(13 examples)

How do you know when a radical problem is done?

1. No radicals can be simplified.Example:

2. There are no fractions in the radical.Example:

3. There are no radicals in the denominator.Example:

8

1

4

1

5

Product Property of Radicals For any numbers a and b where

and , a0

ab a b

b0

aaa

163 16 3

48

4 3

1. Simplify

Find a perfect square that goes into 48.

48

2. Simplify

Find a perfect square that goes into 147. 147

147 349

147 349

147 7 3

2 3 6

3. Simplify 216

2 108

66

2 54

6 9

4. Simplify

Find a perfect square that goes into 605.

605

121 5

121 5

11 5

5. Simplify

1. .

2. .

3. .

4. .

2 18

72

3 8

6 236 2

362 36 2

6. Simplify 77

6b. Simplify 2x

xxxAs a general rule,

divide the exponent by two. The remainder stays in the radical.

7

7. Simplify 49x2

249 x

x7

8. Simplify 15a

aaa 77

aa7

aa 14As a general rule, divide the exponent by two. The remainder stays in the radical.

9. Simplify 258x

xxx 121224

2524 x

xx 22 12

As a general rule, divide the exponent by two. The remainder stays in the radical.

10. Simplify 369x

1. 3x6

2. 3x18

3. 9x6

4. 9x18

As a general rule, divide the exponent by two. The remainder stays in the radical.

Multiply the radicals.

11. Simplify 6 10

60

4 154 152 15

12. Simplify 2 14 3 21

Multiply the coefficients and radicals.

6 294

6 49 66 649

42 6

6 67

13. Simplify

1. .

2. .

3. .

4. .

24 3x44 3x

2 48x448x

36 8x x

SWBAT…simplify radicals using the quotient of property of radicals Fri, 3/16

Agenda 1. WU (10 min)2. Lesson on quotient property of radicals – 5 examples (20 min)3. Lesson on adding and subtracting radicals – 6 examples (15 min)

Simplify:

HW #7: Product & Quotient Property of Radicals

Quotient Property of Radicals

(5 examples)

Quotient Property of Radicals

For any numbers a and b where and , a0 b0

ab

a

b

Examples:

1. 716

2. 3225

7

16

74

32

25

325

4 2

5

Rationalizing the denominator

53

Rationalizing the denominator means to remove any radicals from the denominator.

3. Simplify

5

3

3

3

153

4. Simplify

2

3

2

2

2

6

Simplify

3.

5

2 2

2

2

5 222

5 24

5 2

2 45.

How do you know when a radical problem is done?

1. No radicals can be simplified.Example:

2. There are no fractions in the radical.Example:

3. There are no radicals in the denominator.Example:

8

1

4

1

5

1n na a

= 6

= 31416 = 2

Adding and Subtracting Radicals(6 examples)

Sums and DifferencesThe previous rules allowed us to split radicals that had a radicand which was a product or a quotient.

However, we can NOT split sums or differences.

baba

baba

373 38

24210 26

35 Simplified

Adding and Subtracting Radicals

Ex 1

We can only combine terms with radicals if we have like radicals

Ex 2

Ex 3

Adding and Subtracting Radicals

737576

7)356( 78

Ex 4

Simplify the following radical expression.

331275 3334325

3334325

333235

3325 36

Ex 5

Adding and Subtracting Radicals

=5 6 3 4 6 25 6

=5 6 6 65 6

=4 6

15024365 Ex 6