Question

Prove that root 5 + roo 7 is irrational no

Answer 1

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

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Answer 2

LET 5+ROOT 7=RATIONAL NUMBER
5+ROOT 7=P/Q, WHERE P AND Q ARE some integer and q is not equal to zero...
5+root 7=p/q
Root 7=p/q-5
Root 7=p-5q/q
Here irrational number is equal to rational number which is never be possible
so our assumption is wrong that 5+root7 is rational number
Therefore 5+root7 is a irrational number.


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