prove that root 5 + root 7 is an irrational no.

can u please elaborate the answer venkat

let us assume that root 7 and root 5 are rational
then root 7 +root 5 = a/b where a and b are co primes 
then square on both sides 
(root 7 +root 5)square = a /bwhole square
2xroot 35= a/b whole square -12
root 35 = 1/2(a/b whole square -12)
RHS is rational
but root 35 is irrational as root 7 and root 7 are irrational 
this contradiction has arisen due to our incorrect assumption 
thus root 7 +root 5 is irrational 
hence the proof
 

√5+√7=a/b where a and b are co primes Squaring on both sides (√5+√7)whole square =(a/b)whole square (√5+√7)should be squared with the formula (a+b)the whole square =a square +b square+2ab Then 5+7+2√35=(a/b)whole square 2√35=(a/b)whole square +5+7 2.√35=(a/b)whole square-12 √35=1/2(a/b)whole square -12 On rhs we have a rational number but √35 is a irrational number. This contradicts our assumption. Hence our assumption is wrong. √5+√7 is irrational

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