Question

Show that 2+3 root2 Divided by 7 is not a rational number given that root 2 is an irrational number

Answer 1

let 2+3√2/7 be a rational number

therefore, 2+3√2/7 =p/q [ where q & p are co-prime and q is not equal to 0]

2+3√2 = p×7/q

2+3√2= 7p/q

3√2 = 7p-2/q

3√2= 7p-2q/q

√2= 7p-2q/3q

since √2 is an irrational number and p, q, 7 and 3 are rational numbers, it contradicts our assumption, therefore 2+3√2/7 is an irrational number

(by assumption method)