Prove that if x is odd, then $x^{2}$ is also odd.

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Solution

Let $x = 3$ ,
Then $x^{2} = (3)^{2} = 9$
If $x = 5$ ,
Then $x^{2} = (5)^{2} = 25$
If $x = 7$ ,
Then $x^{2} = (7)^{2} = 49$
So, if $x$ is odd, then the digit in the units place of the resultant number is odd.
Hence, $x^{2}$ is also odd.

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