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SQUARES AND SQUARE ROOTS

Learn about perfect squares and their properties, such as the digits at the units place, the number of zeros at the end, and the sum of consecutive odd numbers. Discover examples and rules for identifying perfect squares.

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SQUARES AND SQUARE ROOTS

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  1. SQUARES AND SQUARE ROOTS

  2. SQUARE OF A RATIONAL NUMBER

  3. Perfect square • A number is called a perfect square if it is the square of a number. • Examples: • 1,4,9,16,25… are called perfect squares.

  4. Properties of square numbers • Property 1: The numbers having 2,3,7, or 8 at the units place are not perfect squares.

  5. Properties of square numbers Property 2: • If a number has 1 or 9 in its units place then its square ends in 1. And 1+9=10 • If a number has 2 or 8in its units place then its square ends in 4. And 2+8=10 • If a number has 3 or 7 in its units place then its square ends in 9. And 3+7=10 • If a number has 4 or 6 in its units place then its square ends in 6. And 4+6=10 • If a number has 0 in its units place then its square ends in 0.

  6. Properties of square numbers Property 3: • A number which has odd number of zeros at the end is never a perfect square. • Example: 10,1000 are not perfect squares. Property 4: • Squares of even numbers are even and squares of odd numbers are odd. • Example:

  7. Property 5: • The number of digits in the square of an n-digit number is either 2n-1 or 2n. • Example: the square of 1-digit number is either 1 or 2.

  8. Property 6: • The square of a number is equal to the sum of that many consecutive odd numbers starting from 1. • Example: • 1 =1= • 1+3 =4= • 1+3+5 =9= • 1+3+5+7 =16=

  9. Property 7: • When any two consecutive numbers are squared, the number of numbers between these squares will be twice the lower number. • Example: • Between

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