5.6 radical expressions rationalizing the denominator like radical expressions conjugates
TRANSCRIPT
5.6 Radical 5.6 Radical ExpressionsExpressions
Rationalizing the denominatorRationalizing the denominator
Like radical expressionsLike radical expressions
ConjugatesConjugates
Product Property of Radicals
If you have the same index, then you can multiply the radicands.
333 2054
3557
Product Property of Radicals
Also, go the other way, the simplify radical expressions
27
49298
Simplify
9425 ba
Simplify
bba
bba
ba
42
84
94
5
25
25
Quotient Property of Radicals
Quotients can be broken apart.
5
1
25
1
25
1
Some rules about Radicals
Reduce them to the lowest index.
224 4 24
Some rules about Radicals
Radicals can not have fractions in them.
This is called Rationalizing the denominator.
5
10
25
10
25
10
5
5
5
2
5
2
Some rules about Radicals
Radicals can not be in the denominator.
No tents in the basement.
3
34
9
34
3
3
3
4
3
4
Simplify
7
8
x
y
Simplify
8
8
7
8
7
8
x
xy
x
x
x
y
x
y
Simplify
4
4
8
8
8
8
7
8
7
8
x
xy
x
xy
x
xy
x
x
x
y
x
y
Simplify
32
2
23
3
3
3
2
9
2
x
x
xx
Simplify
3 33
3 2
333
2
32
2
23
3
6
3
6
3
3
3
2
9
2
x
x
x
x
x
x
xx
Simplify
x
x
x
x
x
x
x
x
xx
3
6
3
6
3
6
3
3
3
2
9
2
3 2
3 33
3 2
333
2
32
2
23
Multiply Radicals
You can only multiply radicals if they have the same index.
aaa
aaa
50105105
10005101005
3 33
3 333 2
Adding and Subtract Radicals
If radical are to the same index and have the same radicand, then they are like radical expressions. Like radicals can be added or subtracted.
666
333
122127125
7117675
Simplify
Simplify radicals first.
204805453
Simplify
Simplify radicals first.
5445165593
204805453
Simplify
Simplify radicals first.
524545533
5445165593
204805453
Simplify
Simplify radicals first.
535852059
524545533
5445165593
204805453
Multiply Radicals
Remember foiling
335332
Multiply Radicals
Remember foiling
353533332323
335332
Multiply Radicals
Remember foiling
153599236
353533332323
335332
Multiply Radicals
Remember foiling
1535963615359)3(236
153599236
353533332323
335332
Simplify
724724
Simplify
17493249)2(16
49228228416
724724
Conjugate
You can not have radicals in the denominator. We have to use the conjugate to rational the denominator in fractions.
54
3
Conjugate
You can not have radicals in the denominator. We have to use the conjugate to rational the denominator in fractions.
54
54
54
3
54
3
Conjugate
Conjugate
You can not have radicals in the denominator. We have to use the conjugate to rational the denominator in fractions.
11
5312
2516
5312
54
54
54
3
54
3
Simplify
Use the conjugate34
32
Simplify
Use the conjugate
13
3611
316
3611
3343416
)3(34328
34
34
34
32
34
32
HomeworkHomework
Page 254 – 255Page 254 – 255
##15 – 49 odd15 – 49 odd
57,5857,58
HomeworkHomework
Page 254 – 256Page 254 – 256
##16 – 48 even16 – 48 even
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