Question

Prove that 5-2/7 root3 is irrational

Answer 1

let 5-2/7√3 be rational no.
therefore
5-2/7√3=p/q
(where p and q are co prime)
2/7√3=5-p/q
2/7√3=5q-p/q
√3=7(5q-p)/2q
here 7,5,2,q,and p are integers.
therefore 7(5q-p)/2q is rational
therefore √3 is rational no
but this contradicts the fact that √3 is irrational no
therefore 5-2/7√3 is irrational no.
hence proved

Answer 2

prove that 1_2-rote 5 is irrational number