Question

Prove that √3+√5 is a irrational number.

Answer 1

Let √ 3 + √ 5 be rational

√ 3 + √5 = P/q

(√3 +√5) sq=(P/q)sq

3 +5 + 2 √15 = P²/q²

√ I5 = (P² / q² -7) 1/2

RHS is rational as all are integers

⇒ LHS is also rational but √ 15 is irrational

⇒ √3 + √ 5 is irrational

Answer 2

Answer:

in the attachment u can understand easily

root15 you can see it is in the p by q

but we know that root15 is an irrational number

so our contradiction is wrong

therefore the given number is an irrational number

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