prove that √2+√3 is irrational
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Let √2+√3 be rational
So √2+√3=p/q,
√2=p/q-√3
Squaring both side,
(√2)^2=(p^2/q^2-√3^2)
2=p^2/q^2-2p/q×(√3)+3
-1=p^2/q^2-2p/q×√3
2p/q×√3=p^2/q^2+1
2p/q×√3=(p^2+q^2)/q^2
2p×√3=(p^2+q^2)/q
√3=(p^2+q^2)/2pq
Irrational=rational , which is not possible.
So our supposition is wrong
Hence,√2+√3
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