(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove or disprove the statement:

13 + 2√6 is an irrational number

Given that √6 is irrational

2. Relevant equations

Rational number = p/q where p and q are integers

3. The attempt at a solution

Assume that 13 + 2√6 is a rational number

Rational number = p/q where p and q are integers

Let 13 = n where n is an integer

Let 2√6 = x

x + n = p/q

x = ( p/q) – n

x = (p – qn)/q

We have shown that x can be expressed as a ratio of two integers. This is a contradiction because we know that x is irrational. Therefore, the statement: 13 + 2√6 is an irrational number is proven true.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof by contradiction

**Physics Forums | Science Articles, Homework Help, Discussion**