Question

Prove that there is a positive number c such that square c = 2

Answer 1

Is this for an abstract algebra class?

Answer 2

No calculus 1
Hint: use intermediate value theorem

Answer 3

I think the point is to show that the function:
\[f(x) = x^2 -2\]
has a zero

Answer 4

Because, for instance, when x=1, the function is less than zero and when x=2, the function is greater than zero. So, via IVT there is at least one point where the function equals zero.

Answer 5

Also, your answer may entail proving that said function is CONTINUOUS... make sense?