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SQUARES AND SQUARE ROOTS

SQUARES AND SQUARE ROOTS. SQUARE OF A RATIONAL NUMBER. 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. Properties of square numbers. Property 1:

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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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