Mathematics: Perfect Squares and Long Division Method

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:
  1. Divide the number by a series of perfect squares (starting from 1) to find the closest perfect square.
  2. Find the square root of the perfect square.
  3. 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.

Learn about the properties of perfect squares and the steps to find the square root of a number using the Long Division Method.