algebra 12.2 operations with radical expressions √
TRANSCRIPT
Algebra12.2
Operations with Radical Expressions √
Review: Simplifying √ Expressions
1. Factor terms under the radical.Find the largest perfect square factor(s).Take square roots outside.
2. Rewrite in simplified form.
72 2 36 6 2
240 2 2 2 2 3 5 4 15
Prime factorization can be useful
Warm-Up: You try.
28 4 7 2 7
84 2 2 3 7 2 21
90 9 10 3 10
150 6 25 5 6
5 2 7 3 8 2
Adding and Subtracting Radicals
You can add and subtract terms that have the same radicand.radicand
These are LIKE TERMS.
13 2 7 3
Add and Subtract: You try.
3 7 5 7 10 7 8 7
2 2 5 6 2 4 2 5
8 5 125 13 5
Simplify each radical term first
8 5 5 5
Add and Subtract: Simplify each term first.
4 3 27 300
11 3
4 3 9 3 100 3
4 3 3 3 10 3
50 2 2 25 2
5 2 2 6 2
Multiplying Radicals
12 5 3 305 36
6 4 10 6 5 8
12 10
6 40
1. Multiply terms outside the radical together.
2. Multiply terms inside the radical together.
3. Simplify.
5 6
6 2 10
Multiplying Radicals
You can multiply using distributive property and FOIL.
3 (7 3 )
5 2 4
7 3 3
(6 2 )(6 2)
2 (5 8)
34
36
5 2 16
6 2 6 2 2
36 2 It’s a DTS!
Multiply: You try.
5 (2 5 ) 2 5 5
2( 2 5 )
9 4 5
( 2 5 )( 2 5 )
4 2 5 2 5 5
(5 7 )(5 7)
It’s a PST!
25 7 18
Dividing to Simplify Radicals
2
32 3
3
3
3
No radicals in the denominator allowed
Denominators must be “rationalized.”
Multiply by 1in the form of
√
√
15
515 5
5
5
5 3 5
3
1
Using the Conjugate to Simplify
Conjugate The other part of a DTS
Expression Conjugate Product
( 2 5 ) ( 2 5 ) 4 5 1
(10 2 ) (10 2 ) 100 2 98
( 10 6) ( 10 6) 10 36 26
The radical “goes away” every time
Dividing to Simplify Radicals
2
5 310 2 3
25 3
5 3
5 3
Multiply by 1in the form of
5 3
11
conjugate
conjugate
10 2 3
22
5 1
11
Simplify: You try.
6
23 2
5
55
4
2 3 8 4 3
Summary:
To ADD and SUBTRACT COMBINE LIKE TERMS
To MULTIPLY “Outside” NUMBERS x NUMBERS
“Inside” NUMBERS x NUMBERS
DISTRIBUTE and FOIL
To DIVIDE “Rationalize” denominator using
1Use conjugate
ALWAYS SIMPLIFY AT THE END IF YOU CAN
Homework
pg. 719 #5-11 odd #19-49 odd