www.iTutoring.com -­‐ NOTES Simplifying Radical (Square Root) Expressions (Product Property) Name _________________________________ Date ___________________ Period _______ Product Property for Square Roots
For every number m ≥ 0 and n ≥ 0,
m·n = m · n
35 =
5·7 =
Method 1: Prime Factorization
Express the radicand (under radical sign)
as a product of prime factors
5 ·
7
Method 2: Perfect Squares
Express the radicand (under radical sign)
as a product of its largest perfect square
Prime factors must “come out” in pairs
24
Method 1: Prime Factorization
24
Method 2: Perfect Squares
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
24
18
Method 1: Prime Factorization
Method 2: Perfect Squares
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
18
18
72
Method 1: Prime Factorization
72
Method 2: Perfect Squares
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
72
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Simplifying Radical (Square Root) Expressions (Product Property) Pg. 2 72
Method 1: Prime Factorization
Method 2: Perfect Squares
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
72
72
20x2y
Method 1: Prime Factorization
20x2y
Method 2: Perfect Squares
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
20x2y
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Simplifying Radical (Square Root) Expressions (Product Property) Pg. 3 12a3b5
Method 1: Prime Factorization
Method 2: Perfect Squares
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
12a3b5
12a3b5
Product Property for Square Roots
For every number m ≥ 0 and n ≥ 0,
m·n = m · n
35 =
5·7 =
Method 1: Prime Factorization
Express the radicand (under radical sign)
as a product of prime factors
5 ·
7
Method 2: Perfect Squares
Express the radicand (under radical sign)
as a product of its largest perfect square
Prime factors must “come out” in pairs
© iTutoring.com
Simplifying Radical (Square Root) Expressions (Product Property) Pg. 4