Question

prove that 7-3√5 is an irrational given that √5 is irrational​

Answer 1

let 7 - 3underoot 5 = a/ b

=> 7 - 3 underoot 5 = a /b

=> 3 underoot 5 = 7b / a

=> underoot 5 = 7b/ 3a

since underoot 5 is irrational no. ( given)

=> 7b/ 3a is also irrational no.

hence

7 - 3 underoot 5 is also irrational

PROVED.