# Proof by contradiction

1. Jun 12, 2010

### Brooke73

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.

2. Jun 12, 2010

### Tedjn

Correct idea, but x = 2√6, and you are given that √6 is irrational.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Proof contradiction Date
Proof by contradiction Jan 29, 2018
Adequate proof? Dec 10, 2016
Linear Algebra with Proof by Contradiction Aug 24, 2016
Proof by Contradiction Aug 24, 2016
Proof by Contradiction Mar 15, 2016