Questions and Answers
What is the property of the square of a positive number?
It is always positive
The long division method is used to find the cube root of a number.
False
What is the formula for (a + b)^2?
a^2 + 2ab + b^2
A perfect square is a number that can be expressed as the __________ of an integer.
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Match the following properties with their corresponding operations:
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Study Notes
Perfect Squares
- A perfect square is a number that can be expressed as the square of an integer.
- Examples: 1, 4, 9, 16, ...
- Properties:
- The square of an even number is even.
- The square of an odd number is odd.
- The square of a positive number is positive.
- The square of a negative number is positive.
Long Division Method
- A method used to find the square root of a number.
- Steps:
- Divide the number by a series of perfect squares (starting from 1) to find the closest perfect square.
- Find the square root of the perfect square.
- Use the result as an estimate for the square root of the original number.
Squaring Numbers
- Squaring a number means multiplying it by itself.
- Example: 3^2 = 3 × 3 = 9
- Properties:
- (a × b)^2 = a^2 × b^2
- (a + b)^2 = a^2 + 2ab + b^2
- (a - b)^2 = a^2 - 2ab + b^2
Note: These notes cover the basics of perfect squares, the long division method for finding square roots, and the properties of squaring numbers.
Perfect Squares
- A perfect square is a number that can be expressed as the square of an integer.
- Examples of perfect squares include 1, 4, 9, 16, and so on.
- The square of an even number is always even.
- The square of an odd number is always odd.
- The square of a positive number is always positive.
- The square of a negative number is always positive.
Long Division Method
- The long division method is used to find the square root of a number.
- The method involves dividing the number by a series of perfect squares starting from 1.
- The result is the closest perfect square to the original number.
- The square root of the perfect square is used as an estimate for the square root of the original number.
Squaring Numbers
- Squaring a number means multiplying it by itself.
- Example: 3^2 = 3 × 3 = 9.
- The property (a × b)^2 = a^2 × b^2 applies when squaring the product of two numbers.
- The property (a + b)^2 = a^2 + 2ab + b^2 applies when squaring the sum of two numbers.
- The property (a - b)^2 = a^2 - 2ab + b^2 applies when squaring the difference of two numbers.
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