Question

Please help me! Zoe's Conjecture: When any number is multiplied by itself, the product will be greater than this starting number.For example, 3 x 3 = 9, the product is greater than the starting number 3 Sage disagreed with Zoe's conjecture. Sage pointed out that 1/3 x 1/3= 1/9 is less than 1/3 . How could Zoe's conjecture be improved? Explain any change or changes you would make

Answer 1

When any number greater than 1 is multiplied by itself, the product will be greater than this starting number

Explanation:

Required: Improve Zoe's conjecture

Zoe's example of 3 * 3 = 9. implies that Zoe's conjecture is only correct for positive numbers greater than 1.

i.e.

`x^2>x*x` if
`x > 1`

So, the conjecture can be improved by limiting Zoe's statement to only numbers greater than 1

In other words:

When any number greater than 1 is multiplied by itself, the product will be greater than this starting number