Question

Show
that root 5 - root 7 is irrational​

Answer 1

Answer:

Because in number is given√5-√7,

√5-√7)(√5+√7)

(√5) sq-(√7)sq

5-7

-2

therefore√5-√7is are irrational number

Answer 2

Answer:

let √5-7 is rational number

let p&q are co-primes

squaring on both sides (s.o.b.s)

(√5-7) square and (p/q) square

(√5-7) and (p/q) will remain

(√5-6/q)and p

transpose -6 to that's side we will get (+6/p)

and transpose q we will get( 6/p_q) √5 is in RHS side so for every integer irrational should be LHS

so assumptions is wrong √5-7 is rational number

HENCE PROVED