Lesson 4 square numbers

Lesson 4 square numbers

• 1.
  SQUARE NUMBERS ALAN S.ABERILLA
• 2.
  When a numberis multiplied by itself, the resultant is called a ‘SQUARE NUMBER’. In geometry, a square has all its sides equal. Therefore the area of the square is equal to the square of its side. Area of a square = Side × Side Therefore, we can say; Square number = a × a= a2 If we express a number (x) in terms of the square of any natural number such as a2, then x is a square number. For example, 100 can be expressed as 10 × 10 = 102, where 10 is a natural number, therefore 100 is a square number. Whereas, the number 45 cannot be called a square number because it is the product of numbers 9 and 5. The number is not multiplied by itself. Square numbers can also be called as perfect square numbers.
• 3.
  Odd and Evensquare numbers  Squares of even numbers are even, i.e, (2n)2 = 4n2.  Squares of odd numbers are odd, i.e, (2n + 1)2 = 4(n2 + n) + 1.  Since every odd square is of the form 4n + 1, the odd numbers that are of the form 4n + 3 are not square numbers. Properties of Square Numbers The following are the properties of the square numbers: 1. A number with 2, 3, 7 or 8 at unit’s place should never be a perfect square. In other words, none of the square numbers ends in 2, 3, 7 or 8. 2. If the number of zeros at the end is even, then the
• 4.
  3. If theeven numbers are squared, it always gives even numbers. Also, if the odd numbers are squared, it always gives odd numbers. 4. If the natural numbers other than one is squared, it should be either a multiple of 3 or exceeds a multiple of 3 by 1. 5. If the natural numbers other than one is squared, it should be either a multiple of 4 or exceeds a multiple of 4 by 1. 6. It is noted that the unit’s digit of the square of a natural number is equal to the unit’s digit of the square of the digit at unit’s place of the given natural number.
• 5.
  7. There aren natural numbers, say p and q such that p 2 = 2q 2 8. For every natural number n, we can write it as: (n + 1) 2 – n 2 = ( n + 1) + n.. 9. If a number n is squared, it equals to the sum of first n odd natural numbers. 10. For any natural number, say ”n” which is greater than 1, we can say that (2n, n 2 – 1, n 2 + 1) should be a Pythagorean triplet. Note: Numbers such as 1, 4, 9, 25, 49, etc. are special numbers as these are the products of a number by itself.
• 6.
  ACTIVITY 3: From thelist above, enumerate the special numbers (between 02=0 up to 302=900 only) Use short bond paper (handwritten or computerized) – utilize the folder of assignment 1