Proving 13 + 2√6 is an Irrational Number with Proof by Contradiction

[Brooke73]

Homework Statement

Prove or disprove the statement:
13 + 2√6 is an irrational number
Given that √6 is irrational

Homework Equations

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

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.

 

[Tedjn]

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