2. Prove that 3 + 2√5 is irrational

Assume that 3 + 2√5 is rational.

Since 3 is rational, subtracting 3 from both sides:
2√5 is rational.

Dividing both sides by 2:
√5 is rational.

But this contradicts the result that √5 is irrational.

Therefore, 3 + 2√5 is irrational.

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