- #1
tuttleforty77
- 9
- 0
Homework Statement
Prove that at least one of 2*10500 + 15 or 2*10500 + 16 is not a perfect square. Can you say specifically which one is not a perfect square?
Consider the proof that √2 is irrational. Could you repeat the same proof for √3? What about √4?
Homework Equations
n/a
The Attempt at a Solution
For the first problem I have no clue where to start. I'm thinking it has something to do with the +15 and +16 at the end, but I'm not 100% sure on that.
For the second one I know that you can prove that the √n is irrational for all integers that are not a perfect square, I'm just not sure how to prove it. Would it be similar to the proof of the √2 being irrational, just tweaked a bit because of the variable n?
√n = p / q (where p / q is expressed in its lowest terms)
n = p2 / q2
n * q2 = p2
and this is where I get stumped :(