Step-by-step explanation:
To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.
Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0
⇒ 3 + 2√5 = p/ q
⇒ 2√5 = p/ q - 3
⇒ √5 = (p - 3q ) / 2q
⇒ (p - 3q ) / 2 q is a rational number.
However, √5 is an irrational number
This leads to a contradiction that 3 + 2√5 is a rational number.
