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Prove that 3+2√5 is irrational​

1 Answer

2 votes

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.

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