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Brooke73
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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.