A perfect square refers to any number multiplied by itself.

(i) Square “Pyramids”

The following sets of square numbers can be arranged in pyramidal patterns.

perfect-squares-1

(ii) Consecutive Odd Numbers

Square numbers can be written as a series of consecutive odd numbers.

12 = 1 = 1

22 = 4 = 1 + 3

32 = 9 = 1 + 3 + 5

42 = 16 = 1 + 3 + 5 + 7

52 = 25 = 1 + 3 + 5 + 7 + 9

62 = 36 = 1 + 3 + 5 + 7 + 9 + 11

72 = 49 = 1 + 3 + 5 + 7 + 9 + 11 + 13

82 = 64 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

92 = 81 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

(iii) Magic Perfect Square

Here is an extraordinary magic square made up entirely of perfect squares. Find its Magic Sums.

perfect-squares-3

Click to see solution..

Solution

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