Squares

Squares

Properties of square numbers

How to identify square numbers?

• A square number can always be expressed as the product of pairs of equal prime factors

• A number having 2,3,7 or 8 at its units place is never a square number

• A number ending in an odd number of zeros is never a perfect square

Multiple Select

Which of the following natural numbers are perfect squares?

• 729

• 5488

• 1024

• 243

Multiple Select

The square of which of the following numbers will be even number

• 573

• 4096

• 8267

• 37916

Numbers between consecutive square numbers

• There are 2n non-square numbers between the squares of two consecutive numbers n and n+1

Adding odd numbers

• The sum of first n odd natural numbers is n²

Square of odd numbers as a sum of consecutive numbers

• We can express the square of any odd number greater than 1 as the sum of two consecutive natural numbers

• 3² = 9 = 4+5

• 5² = 25 = 12+13

7² =49 = 24+25

7²=49

49 = (49 - 1)/2 + (49 + 1)/2

49 = 24 + 25

Therefore 7² = 24 + 25

11² =121 = 60+61

11²=121

121 = (121 - 1)/2 + (121 + 1)/2

121 = 60 + 61

Therefore 11² = 60 + 61