# Prove that 3 + 2√5 is an irrational number.

Rational numbers are integers that are expressed in the form of p / q where p and q are both co-prime numbers and q is non zero.

## Answer: Hence proved that 3 + 2√5 is an irrational number

Let's find if 3 + 2√5 is irrational.

**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.

### Thus, 3 + 2√5 is an irrational number by contradiction method.

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