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Questions and Answers
What is the sum of the squares of 5 and 6?
What is the sum of the squares of 5 and 6?
61
What is the square of the sum of 4 and 3?
What is the square of the sum of 4 and 3?
49
Identify the smallest two-digit square number.
Identify the smallest two-digit square number.
16
What is the difference between the squares of 10 and 8?
What is the difference between the squares of 10 and 8?
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Which perfect square is represented by 7², and how is it represented numerically?
Which perfect square is represented by 7², and how is it represented numerically?
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Study Notes
Perfect Squares
- Perfect squares are numbers obtained by squaring integers.
- The square of 1 is 1 (1² = 1).
- The series runs from the square of 1 through to the square of 60.
Key Perfect Squares
- Common examples include:
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81
- 10² = 100
Larger Perfect Squares
- Larger integers continue the pattern:
- 11² = 121, 12² = 144, 13² = 169
- Up to 20² = 400
- The sequence proceeds up to 60² = 3600.
Quadratic Growth
- The difference between successive squares increases linearly:
- For example, the difference between 1² (1) and 2² (4) is 3; between 2² (4) and 3² (9) is 5, and so forth.
Application in Mathematics
- Perfect squares appear frequently in geometry, algebra, and number theory, establishing foundations for quadratic equations and concepts like Pythagorean triple.
Memorization Tips
- Create a visual chart of squares for quick reference.
- Understand and recognize the patterns in the last digits.
- Practice mental math for smaller squares to improve speed with larger numbers.
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