- 1
Suppose 2=qproot 2 equals p over q, a fraction in lowest terms.
Skipped the primer on proof by contradiction — your skill check shows you have it.
- 2
Squaring, p2=2q2p squared equals 2 q squared. So p2p squared is even, and so is pp. Write p=2kp equals 2 k.
- 3
Then 4k2=2q24 k squared equals 2 q squared, so q2=2k2q squared equals 2 k squared and qq is even too.
Next, you explain why p² even forces p even. In your own words.
- 4
Both are even, so the fraction was not in lowest terms. The assumption fails. ∎