Prove that 3 + root 5 is irrational
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Let us suppose 3+√5 is rational.
=>3+√5 is in the form of p/q where p and q are integers and q is not =0
=>√5=p/q-3
=>√5=p-3q/q
as p, q and 3 are integers p-3q/3 is a rational number.
=>√5 is a rational number.
But we know that √5 is an irrational number.
This is an contradiction.
This contradiction has arisen because of our wrong assumption that 3+√5 is a rational number.
Hence 3+√5 is an irrational number.
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