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Questions and Answers
What is the square root of a perfect square?
What is the square root of a perfect square?
- Always an integer (correct)
- Always a rational number
- Always a prime number
- Always an odd number
Which of the following is a characteristic of perfect squares?
Which of the following is a characteristic of perfect squares?
- They always end in 2 or 3
- They always end in 0, 1, 4, 5, 6, or 9 (correct)
- They always end in 10 or 11
- They always end in 7 or 8
What is the formula to calculate a perfect square?
What is the formula to calculate a perfect square?
- Multiply the number by itself (correct)
- Subtract 1 from the number
- Add 2 to the number
- Divide the number by 2
What is the result of multiplying two perfect squares?
What is the result of multiplying two perfect squares?
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What is one of the real-world applications of perfect squares?
What is one of the real-world applications of perfect squares?
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What is the definition of a perfect square?
What is the definition of a perfect square?
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Study Notes
Perfect Squares
Definition
A perfect square is an integer that can be expressed as the square of another integer. For example, 16 is a perfect square because it can be expressed as 4^2.
Properties
- The square root of a perfect square is always an integer.
- Perfect squares always end in 0, 1, 4, 5, 6, or 9.
- The sum of two perfect squares is not always a perfect square.
- The product of two perfect squares is always a perfect square.
Examples
- 1, 4, 9, 16, 25, 36, 49, 64, 81, ...
- These numbers can be expressed as:
- 1 = 1^2
- 4 = 2^2
- 9 = 3^2
- 16 = 4^2
- 25 = 5^2
- 36 = 6^2
- 49 = 7^2
- 64 = 8^2
- 81 = 9^2
Calculating Perfect Squares
- To calculate a perfect square, simply square the number (multiply it by itself).
- For example, to calculate 5^2, multiply 5 by 5 to get 25.
Real-World Applications
- Perfect squares are used in geometry to calculate areas of shapes.
- They are also used in algebra to solve equations and inequalities.
- Perfect squares have many applications in computer science, physics, and engineering.
Perfect Squares
Definition
- A perfect square is an integer that can be expressed as the square of another integer.
Properties
- The square root of a perfect square is always an integer.
- Perfect squares always end in 0, 1, 4, 5, 6, or 9.
- The sum of two perfect squares is not always a perfect square.
- The product of two perfect squares is always a perfect square.
Examples
- Examples of perfect squares include 1, 4, 9, 16, 25, 36, 49, 64, 81, ...
- These numbers can be expressed as squares of integers, such as 1 = 1^2, 4 = 2^2, 9 = 3^2, and so on.
Calculating Perfect Squares
- To calculate a perfect square, multiply the number by itself.
- For example, to calculate 5^2, multiply 5 by 5 to get 25.
Real-World Applications
- Perfect squares are used in geometry to calculate areas of shapes.
- They are used in algebra to solve equations and inequalities.
- Perfect squares have many applications in computer science, physics, and engineering.
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Description
Learn about the definition, properties, and examples of perfect squares, including their integer roots and unique characteristics.
