Question

Prove that √5+√3 is irrational

Answer 1

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Answer 2

♧♧HERE IS YOUR ANSWER♧♧

We will prove it by contradiction.

Let us consider :

√5 + √3 = p/q, where p and q are integers such that q ≠ 0.

Now,

√5 + √3 = p/q

=> √5 = p/q - √3

Squaring, we get :

(√5)² = (p/q - √3)²

=> 5 = (p²/q²) - 2√3(p/q) + 3

=> 2√3(p/q) = (p²/q²) - 2

=> √3 = p/(2q) - (2q)/p,

which implies that √3 is a rational number.

Thus, √5 + √3 is an irrational number.

Hence, proved.

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