root3+root2 it is rational or irrational with explaining answer
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root3+root2 it is rational or irrational with explaining answer
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Answer:
Step-by-step explanation:
let assume that root3+root2 be a rational number
root3+root2=p/q
root3=p/q-root2
By squaring on both sides, root3^2=[p/q-root2]^2
3=p²/q^2-2root2.p/q+2
2root2p/q=p^2/q^2-1
2root2p/q=p^2-q^2/q^2
root2=[p^2-q^2/q^2][q/2p]
root2=p^2-q^2/2pq
root2is a rational number since p^2-q^2/2pq is a rational number
But root 2 is is not a rational number. This leads us to a contradiction.
∴ our assumption that root3+root2 is be rational number is wrong
root3 +root2 is irrational