Prove that √3+√5 is an irrational number

1.	Prove that √3+√5 is an irrational number
Answer» Let the given no. be rational. So there exist co prime integers a and b such that. √3+√5=a/b S.B.S ( √3+√5)^2=a/bSolving this we get the answer Yes Let us assume that √2+√3 is a rational no.√3+√5=p/qP/q-√3=√5Squaring both sides(P/q-√3)2=(√5)2P2/q2-2√3p/q+3=5P2/q2-2√3p/q+3-5P2/q2-2=2√3p/qP2-2q2/q22p/q√3P2-2q2/2pq=√3.This contradicts the fact that √ 3 is a irrational no.So,aur assume was incorrect.Here ,√2+√3is irrational no.

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