Question

prove that root 2 + root 3 is irrational​

Answer 1

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Your Ans is:—

Let √2 + √3 be a rational number.

Then, there exists co-prime positive integers p and q such that

=> √2 + √3 = p/q

=> √2 = p/q – √3

Squaring both sides

=> 2 = p²/q² – 2×p/q×√3 + 3

=> p²/q² + 1 = 2×√3×p/q

=> p² + q²/ 2pq = √3

Since p,q and 2 are integers so √3 is rational

But this contradicts the fact that √3 is irrational

THEREFORE

√2 + √3 is irrational

✌HOPE IT HELPS✌

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