Question

prove that √3 + √2 is irrational​

Answer 1

Answer:

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Answer 2

Let us assume root 3 + root 2 be a rational number

root 3 + roo 2 = p/q where p,q ∈ z,q not equal to 0

root 3 = p/q - root 2

Squaring both side,

(root3)² = (p/q - root2)²

=> 3 = p²/q² - 2 . root 2 . p/q + 2

=> 2 root 2 . p/q = p²/q² + 2 - 3

=> 2 root 2 . p/q = p²/q² - 1

=> 2 (root 2) p/q = (p² - q²)/q²

=> root 2 = (p² - q²/q²)(q/2p)

=> root 2 = p² - q² / 2pq

root 2 is a rational no.

Therefore, p² - q² / 2pq is a rational number.

But root 2 is a irrational number this leads us to a contradiction.

Since, our assumption that root 3 + root 2 is a rational number is wrong.

Root 3 + root 2 is an irrational number

Hope it helps

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