Question

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prove that√3+√5 is irrational..

Answer 1

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let root 3 + root 5 be rational

root 3 + root 5 = P/q

(root 3 + root 5) sq=(P/q)sq

3 +5 + 2 root 15 = P sq/q Sq

root I5 = (Psq / qsq -7) 1/2

RHS is rational as all are integers

⇒ LHS is also rational but root 15 is irrational

⇒ root3 + root 5 is irrational

MARK AS BRAINLIEST

Answer 2

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Let √3+√5 be a rational number.
A rational number can be written in the form of p/q where p,q are integers.
√3+√5 = p/q
√3 = p/q-√5

Squaring on both sides,
(√3)² = (p/q-√5)²
3 = p²/q²+√5²-2(p/q)(√5)
√5×2p/q = p²/q²+5-3
√5 = (p²+2q²)/q² × q/2p
√5 = (p²+2q²)/2pq

p,q are integers then (p²+2q²)/2pq is a rational number.

Then √5 is also a rational number.

But this contradicts the fact that √5 is an irrational number.

So,our supposition is false.

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