m·n = m n · 24
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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
© iTutoring.com 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
© iTutoring.com 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
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
© iTutoring.com 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
© iTutoring.com 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
