Maths-
General
Easy

Question

Make and test a conjecture about the square of odd numbers.

hintHint:

Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

The correct answer is: Hence, we conclude that the square of an odd number will also be an odd number and we have proved this conjecture by deductive reasoning.


    Let’s create a conjecture for the odd numbers 3, 7, 9, and 15. We are asked to make a conjecture about the square of odd numbers.
    So first, do the square of the assumed odd numbers. We got

    32 = 9

    72 = 49

    92 = 81

    152 = 225
    So, we conclude that the square of an odd number will also be an odd number and this is the conjecture.
    Now, let’s see if the conjecture is true or not by deductive reasoning. Let’s say the odd number is x. This odd can be written as
    x = 2k + 1    (where k is some integer)
    Now, squaring both sides

           x2 = (2k+1)2

         = 4k2 + 1 + 4k

         = 4(k2+k) +1
    Take (k2+k) = m, where m is some integer

            x2 = 4m +1
    4m is an even number and adding 1 to 4m will result in an odd number and hence x2 is an odd number.
    Final Answer:
    Hence, we conclude that the square of an odd number will also be an odd number and we have proved this conjecture by deductive reasoning.

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