essential question: what must be true of radical expressions in order to add them, but not multiply...
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Essential Question: What must be true of radical expressions in order to add them, but not multiply them?
UNIT: RADICAL FUNCTIONS7-3: BINOMIAL RADICAL EXPRESSIONS
7-3: Binomial Radical Expressions Just like how you can add and subtract like
terms, you can add and subtract like radicals.
Just like how you can’t add/subtract unlike terms, you can’t add/subtract unlike radicals.
5 3
(5 3)
2
x x
x
x
3 3
3
3
5 3
(5 3)
2
x x
x
x
4 5x y 4 2 5 3
7-3: Binomial Radical Expressions YOUR TURN Add or subtract, if possible:
2 7 3 7
347 5 2 5
4 5xy xy
5 7
9 xy
Not possible
7-3: Binomial Radical Expressions Sometimes radicals can be
added/subtracted, but they need to be simplified first.
6 18 4 8 3 72 6 2 4 2 3 2
6 3 2 4 2
3
2 3 6 2
18 2 8 2 18 2
3 2 2 6
2
6
8
7-3: Binomial Radical Expressions YOUR TURN Simplify
50 3 32 5 18 5 5 4 42 3 2 5 23 3
5 2 12 2 15 2
5 2 3 4 2 5 3 2
2 2
7-3: Binomial Radical Expressions When radicals are in the form of
binomials, they can be multiplied together using FOIL 2
(3 2 5)(2 4 5)
6 16 5 40
46
3 4 5
12 5
2 5 2
4 5
5 4 5
8 5
3 2
16 5
6
7-3: Binomial Radical Expressions YOUR TURN Multiply
22 3 2 3 2 3
2 6 6 3
5 2 6
7-3: Binomial Radical Expressions Assignment
Page 382 Problems 1 – 6, all
7 – 17, odd (show work)
Essential Question: What must be true of radical expressions in order to add them, but not multiply them?
UNIT: RADICAL FUNCTIONS7-3: BINOMIAL RADICAL EXPRESSIONS(DAY 2)
7-3: Binomial Radical Expressions Conjugates
Conjugates are expressions that differ only by the sign between the two terms. Conjugates are used to eliminate radicals in an expression, as the result is an integer.
(2 3)(2 3)
4 3
1
2 3 2 3
7-3: Binomial Radical Expressions YOUR TURN
Multiply each pair of conjugates ( 5 2)( 5 2) (3 7)(3 7)
10 15 2
3
0 3 7 39 7
2
7
7-3: Binomial Radical Expressions Rationalizing the denominator
Recall that when we rationalized the denominator to a single radical expression, we simply multiplied numerator and denominator by that radical:
2
33
3
3
6
7-3: Binomial Radical Expressions Rationalizing the denominator
When dealing with a binomial for a denominator, we multiply numerator and denominator by the denominator’s conjugate
3 5
1 5
3 5 3 3 5 1 5 5
1 5 1 1 5 1 5 5
8 4 5
1 5
1
4
5
5
2
7-3: Binomial Radical Expressions YOUR TURN Rationalize the denominator
6 15
4 15
6 4 15
4 15
15
4 15
39 10 15
24 6 15 4 15 15
16 4 15 4 15 15
39 10 15
1
7-3: Binomial Radical Expressions YOUR TURN Rationalize the denominator
2 3
4 3
2 4 3
4 3
3
4 3
8 2 3 4 3 3
16 4 3 4 3 3
11 6 3
13
7-3: Binomial Radical Expressions Assignment
Page 382 Problems 19 – 26, all (show work)