Question

prove that√3+√5 is an irrational number.

Answer 1

as if we try to solve

$\sqrt{3}$

it will proved as irrational

Answer 2

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HERE COMES YOUR ANSWER.....

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Let us assume that √3+√5 is rational number.

A rational number can be written in the form of a/b where p,q are co-prime no.

√3+√5 = a/b

√3 = a/b-√5

by Squaring on both sides,

(√3)² = (a/b-√5)²

3 = a²/b²+√5²-2(a/b)(√5)

√5×2a/b = a²/b²+5-3

√5 = (a²+2b²)/b² × b/2p

√5 = (a²+2b²)/2ab

a,b are integers then (a²+2b²)/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 assumption is false.

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

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