Maths-
General
Easy

Question

Find a counterexample to show that the following conjecture is false.
Conjecture: The square of any integer is always greater than the integer.

The correct answer is: given statement is false.


    We have given, the square of every integer is always greater than the integer.
    We have to prove that given statement false.
    Number obtained when a number is multiplied by itself three times is called a cube number.
    If m = n², then m is a perfect square  where m and n are natural numbers.
    Example: consider 1
    Square of 1 = 1
    Example: consider 2
    Square of 2 = 4
    Therefore, the square of every natural number is not always greater than the number itself.
    Therefore, given statement is false.

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