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charmedbeauty
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Homework Statement
if n is a positive integer than √(4n-2) is irrational.
Homework Equations
The Attempt at a Solution
√(4n-2) Assume is rational
then by definition of rationality
√(4n-2)=p/q for some integers p,q where q≠0
so √(2(2n-1))=p/q by factoring out the 2 as common
√2 *√(2n-1) =p/q
but 2n-1 is always odd
so √(2n-1) is always odd
now let u=√(2n-1)
but √2*u cannot be factored since √2 is irrational and u is odd.
so √(4n-2)≠p/q
Therefore our assumption must have been wrong therefore
√(4n-2) must be irrational
Is this proof ok??