## Lime 3 years ago Raise your hand if you love Inductive Reasoning! I've wrapped my mind around this one. Choose a counterexample that proves that the conjecture below is false. "Other than the number 1, there are no numbers less than 100 that are both perfect squares and perfect cubes." You have a choice of 36, 64, 16, and 8. So, I have to prove this statement false by providing a number that IS a perfect square. I've come to the conclusion that the answer is 16. Or is this a trick question? 8 is not a perfect square and therefore proves the sentence true?

1. mathslover

64?

2. Armor

You need to find a number that is both a perfect square and a perfect cube. 16 is not a perfect cube, so it isn't a counter example.

3. mathslover

64 = 4^3 and 64 = 8 ^2

4. mathslover

Hence 64 is a counter example to prove the statement wrong

5. Lime

I have to prove the sentence false by giving the correct answer? Isn't that a counter-positive?

6. Lime

Excuse me, *contra-positive.

7. mathslover

yes that proves that the sentence if false... the statement says that there is only one number i.e. 1 which is both perfect square and perfect cube You have to find a number other than "1" which is both perfect square and perfect cube.. i.e. 64 .. which proves the above statement wrong

8. mathslover

Lime .. "read" the question again.. You might have misunderstood the question..

9. Lime

Well explained, thank you. :)

10. mathslover

You r welcome Lime.. Also ... best of luck for your further questions.. You must try to understand these type of questions by reading again and again