Math, asked by niksinghjr, 1 year ago

prove that √2+√3 is irrational

Answers

Answered by shaileshsingh1281
0

Answer:

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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