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let us assume that √5+√6 is rational.
is in the form of p÷q
√5+√6=p/q
√6=p/q - √5
√6= p - √5q/q
squaring on both sides
6=(p -√5q)^2/q^2
substitute RHS
Finally we get RHS is irrational.
BUT LHS is rational
rational can't equal to irrational.
This contradicts that √5+√6 is irrational.
So, our assumption is wrong.
So,√5+√6 is an irrational.
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