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Questions and Answers
What is the first step in calculating the square root of 36 according to Group Alpha's activity?
Which number should Group Gamma first prime factorize?
Which group is assigned the number 4624?
What is the final step in calculating the square root of assigned numbers?
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Which group's activity involves finding the square root of 144?
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What is done after arranging the prime factors into pairs?
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Which pair of numbers is Group Delta assigned?
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What is the common first step in the activities of all groups?
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Study Notes
Calculating Square Roots using Prime Factorization
Task 1: Group Alpha
- Prime factors of 36: 2, 2, 3, 3
- Prime factors of 1296: 2, 2, 2, 2, 3, 3, 3, 3
- Pairing prime factors: (2, 2), (3, 3) for 36 and (2, 2), (2, 2), (3, 3), (3, 3) for 1296
- Taking one number from each pair out of the square root: 2, 3 for 36 and 2, 2, 3, 3 for 1296
- Square roots of 36 and 1296: 6 and 36, respectively
Task 2: Group Gamma
- Prime factors of 81: 3, 3, 3, 3
- Prime factors of 4096: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
- Pairing prime factors: (3, 3), (3, 3) for 81 and (2, 2), (2, 2), (2, 2), (2, 2), (2, 2), (2, 2) for 4096
- Taking one number from each pair out of the square root: 3, 3 for 81 and 2, 2, 2, 2, 2, 2 for 4096
- Square roots of 81 and 4096: 9 and 64, respectively
Task 3: Group Delta
- Prime factors of 64: 2, 2, 2, 2, 2, 2
- Prime factors of 5776: 2, 2, 2, 2, 2, 2, 11, 11
- Pairing prime factors: (2, 2), (2, 2), (2, 2) for 64 and (2, 2), (2, 2), (2, 2), (11, 11) for 5776
- Taking one number from each pair out of the square root: 2, 2, 2 for 64 and 2, 2, 2, 11 for 5776
- Square roots of 64 and 5776: 8 and 76, respectively
Task 4: Group Beta
- Prime factors of 100: 2, 2, 5, 5
- Prime factors of 4624: 2, 2, 2, 2, 17, 17, 17
- Pairing prime factors: (2, 2), (5, 5) for 100 and (2, 2), (2, 2), (17, 17), (17, 17) for 4624
- Taking one number from each pair out of the square root: 2, 5 for 100 and 2, 2, 17, 17 for 4624
- Square roots of 100 and 4624: 10 and 68, respectively
Task 5: Group Zeta
- Prime factors of 144: 2, 2, 2, 2, 3, 3
- Prime factors of 7056: 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 7
- Pairing prime factors: (2, 2), (2, 2), (3, 3) for 144 and (2, 2), (2, 2), (2, 2), (2, 2), (3, 3), (7, 7) for 7056
- Taking one number from each pair out of the square root: 2, 2, 3 for 144 and 2, 2, 2, 2, 3, 7 for 7056
- Square roots of 144 and 7056: 12 and 84, respectively
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Description
Calculate square roots using prime factorization method. Find the square roots of 36 and 1296 by prime factorizing the numbers and arranging the prime factors in pairs.
