- #1
r0bHadz
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Homework Statement
Prove sqrt(3) is irrational
Homework Equations
The Attempt at a Solution
(a/b)^2 = 3 assume a/b is in lowest form
a^2 = 3b^2
so a^2 is of form 3n
whenever n is even, a^2 will be even => a will be even whenever n is even
so a is of form 2l whenever n is even
=> 4l^2 = 3b^2 => 2l/sqrt(3) = b
rewrite as 2((l*sqrt(3))/3) = b
contradiction. Since both a and b are divisible by 2 whenever n is even, sqrt(3) must be irrational for even n, This implies that sqrt(3) is irrational