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

Let's find if 5 + 3 √2 is irrational.

**Explanation:**

To prove that 5 + 3 √2 is an irrational number, we will use contradiction method.

Let us assume that 5 + 3 √2 is a rational number with p and q as co-prime integers and q ≠ 0

⇒ 5 + 3 √2 = p / q

⇒ 3 √2 = (p / q) - 5

⇒ √2 = (p - 5q ) / 3q

⇒ (p - 5q ) / 3q is a rational number

However, we know that √2 is an irrational number

This leads to the contradiction that 5 + 3 √2 is a rational number