Question

prove that √3+√5 is irrational

Answer 1

Hii There!!

Let us assume to the contrary that √3+√5 be rational.

=) √3+√5= p/q
[where p and q are integers having no common factors].


=) (√3+√5)sq = (p/q) sq

=) 3+3+ 2√15 = P sq/q Sq

=) √15 = (Psq / qsq -7) 1/2

=) Here R.H.S. is rational and L.H.S is also rational but √15 is irrational.


=) Hence, √3+√5 is irrational number.


Hope it helps


#DK
<<DEAR P>>

Answer 2

Hey dear!

Here is yr answer......


Let us assume √3+√5 is rational

let √3+√5 = a/b (a, b are any integers)


=> √5 = a/b - √3

Squaring on both sides.......


=> 5 = a²/b² + 3 - 2(a/b)(√3)

=> 5 = a²/b² + 3 - 2√3a/b

=> 2√3a/b = a²/b² + 3 - 5

=> 2√3a/b = a²/b² - 2

=> 2√3a/b = a²-2b²/b²

=> 2√3a = a²-2b²/b

=> √3 = a²-2b²/2ab


For any two integers RHS is rational!

But LHS is irrational...


A rational and irrational are never equal!


So, our assumption is false..


Therefore, √3+√5 is irrational!


Hope it hlpz..