Maths-
General
Easy

Question

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

hintHint:

Take general form and check.

The correct answer is: we get that the square of an odd number is always odd.


    Complete step by step solution:
    The square of an odd number is always an odd number.
    We know that the odd number is always of the form 2n+1
    Let some N = 2n + 1
    On squaring both the sides, we get N squared equals open parentheses 2 n plus 1 close parentheses squared
    not stretchy rightwards double arrow N squared equals 4 n squared plus 4 n plus 1
    On taking common from RHS part, we get N squared equals 2 n left parenthesis 2 n plus 1 right parenthesis plus 1
    not stretchy rightwards double arrow N squared equals 2 n left parenthesis N right parenthesis plus 1 left parenthesis text  since  end text N equals 2 n plus 1 right parenthesis
    not stretchy rightwards double arrow N equals 2 n plus 1
    So we get that the square of an odd number is always odd.
    Note: We can take the form of N = 2n - 1 and then find the square and then also
    we get that the square of an odd number is always odd.

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