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Let us assume 2√3+√5 as rational.
we can get integers a&b in the form a/b.
squaring obs
(2√3+√5)sq= (a/b)sq
(2√3)sq +(√5)sq+2(2√3×√5)= (a)sq/(b)sq
20+5+4+2√15=(a)sq/(b)sq 2√15=(a)sq/(b)sq - 29
since a&b are integers 2√15 is rational
but this contradicts that 2√3+√5 is irrational.
this contradiction has arisen due to the incorrect assumption that 2√3+√5 is rational .
hence it is irrational.
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