# Interesting Aspects of Square Numbers and Square Number Calculations

October 11, 2013

Square numbers like all other mathematical topics can be learned by looking at interesting aspects which make mathematical learning more joyful and interesting.   Sometimes, by just playing around with calculations, you may also discover interesting aspects of calculations and also deepen and sharpen your interest in maths.  Let us look at a few interesting aspects of square number calculations.

1. The following are examples of two squares which when added together give another square number.

9 and 16 which are square numbers when added give 25 another square number, that is, 32 +  42 =  52

=  9  +  16  = 25

Likewise, 36 and 64 when added together give 100 which is another square number, that is,

62 +   82 =  102

=  36  +  64  = 100

Likewise, 81 and 144 are two square numbers which when added together give 225 which is another square number, that is,

92 +    122 = 152

=  81 +  144 = 225

2.   The following are examples of three square numbers which when added together give another   square number, that is,

4, 9 and 36 are three square numbers which when added together give 49 which is another square number, that is,

22 + 32 + 62 =  72

= 4 + 9 + 36 = 49

Likewise, 1, 16 and 64 which when added together give 81, that is,  12 +  42 + 82 = 92

= 1 + 16 + 64 = 81

Likewise, 16, 25, and 400 when added together give 441, that is,  42 + 52 + 202 =212

=  16 + 25 + 400 = 441

3.  Do you know what a palindrome number is?

A palindrome number is a number which reads the  same forwards and backwards and has symmetry.

Let us see examples of palindrome in the form of squares:

Consider 112 = 121 which reads the same forwards and backwards and is an example of a palindrome.

Other examples of square numbers which are palindromes are 222 = 484 and  262 = 676

In the same way, study square numbers in a free flowing manner.

You will be surprised at the interesting aspects of square  number calculations you can find.

photo credit: Leo Reynolds via photopin cc

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