Question

Prove that the following numbers are irrational:
(i) √18
(ii) √14
(iii) 3√2​

Answer 1

let √18 be rational

√18can be written as p/q

√18=p/q

squaring both sides

18=p²/q²

18q²=p²

this mean that 18 divides p²

also 18 divides p

hence 18 divides p there exist an integer equal to 5 divide p let k

p/18=k

p=k*18-----(i)

put(i)in 18q²=p²

18*<q>²=(18k)²

18q²=18*18k²

q²=18k²

this mean that 18 divies q²

also 18 divides q

this mean that p and q have a common factor 18 but a true rational number have co prime integers as its numerator and denominator

therefore we are wrong √18 is irrational

you have to only change digits and the other pattern remains same