swbat…simplify radicals using the product property of radicalswed, 3/14 agenda 1. wu (10 min) 2....
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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