[Verse 1] Let's suppose root two can be reduced To p over q in simplest form A rational fraction, clean and neat Both integers, their bond transformed We'll follow this assumption's trail And watch it crumble, watch it fail [Chorus] Square both sides, the trap unfolds Two equals p squared over q squared Rearrange the story told Two q squared equals p squared there Even numbers multiply Watch the contradiction fly [Verse 2] If two q squared equals p squared now Then p squared must be even, see Which means that p itself is even too So write it as two k, the key Substitute back in our equation Sets the stage for devastation [Chorus] Square both sides, the trap unfolds Two equals p squared over q squared Rearrange the story told Two q squared equals p squared there Even numbers multiply Watch the contradiction fly [Bridge] Two q squared equals four k squared Divide by two, we get q squared equals two k squared Now q squared is even, so q is even too But wait, we said p over q was reduced through and through Both p and q are even now, they share a common two Our simplest form assumption? That assumption wasn't true [Chorus] Square both sides, the trap unfolds Two equals p squared over q squared Contradiction's tale is told Our assumption's torn and bared Rational hopes have said goodbye Root two's irrational, we can't deny [Outro] The suspect's alibi destroyed By perfect logical precision Root two cannot be expressed As any rational decision
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