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Using prime factorization method, find which of the following numbers are perfect squares? 189, 225, 2048, 343, 441, 2961, 11025, 3549 |
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Answer» Since, 189 = 32 × 3 × 7 It cannot be written as pair of two equal factors, so 189 is not a perfect square. Since, 225 = (5 × 5) × (3 × 3) It can be written as pair of two equal factors, so 22 is a perfect square. Since, 2048 = (2 × 2) × (2 × 2) × (2 × 2) (2 × 2) × (2 × 2) × 2 All the factors cannot be written as pair of two equal factors, so 189 is not a perfect square. Since, 343 = (7 × 7) × 7 It cannot be written as pair of two equal factors, so 343 is not a perfect square. Since, 441 = (7 × 7) × (3 × 3) It can be written as pair of two equal factors, so 441 is a perfect square. Since, 2916 = (3 × 3) × (3 × 3) × (3 × 3) × (2 × 2) It can be written as pair of two equal factors, so 2916 is a perfect square. Since, 11025 = (5 × 5) × (3 × 3) × (7 × 7) It can be written as pair of two equal factors, so 11025 is a perfect square. Since, 3549 = (13 × 13) × 3 × 7 It cannot be written as pair of two equal factors, so 3549 is not a perfect square. |
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