Question

Jackie made the following conjecture. The square of a number is always greater than the number. Which choice, if either, is a counterexample to this conjecture?

0.
5
2
=
0.25
0.5
2
=0.25
(
−
5
)
2
=
25
(−5)
2
=25
a. Choice 2 only
b. Choice 1 only
c. Choice 1 and Choice 2
d. Neither Choice 1 nor Choice 2

Answer 1

Choice 1 (0.5 squared equals 0.25) is a counterexample to Jackie's conjecture, as the square is less than the original number, while Choice 2 (-5 squared equals 25) supports the conjecture.

Step-by-step explanation:

The conjecture made by Jackie states that the square of a number is always greater than the number itself. To determine if this conjecture holds true, we must examine the provided choices.

Choice 1: 0.52 = 0.25. Here, we observe that the square of 0.5 is indeed less than 0.5 itself, making it a counterexample to the conjecture.

Choice 2: (-5)2 = 25. In this case, the square of -5 is greater than -5, which aligns with the conjecture and therefore is not a counterexample.

Conclusively, the correct answer identifying a counterexample to the conjecture is Choice 1 only, which demonstrates that the square of a number is not always greater than the number itself.