Question

show that2-3√7 is an irrational number, where √7 is given as irrational number​

Answer 1

Answer:

let 2-3root7 be rational

2-3root7=p/q where p and q are coprime and q not equal to 0

2+p/q=3root7

(2q+p )/q=3root7

2q+p/3q = root 7

as p and q are integers 2q+p/3q is rational number .so root 7 is also rational number

but it contradicts the fact that root 7 is irrational

so our assumption is wrong

hence 2-3root7 is irrational