Question

prove that √3 is irrational number​

Answer 1

Answer:

root(3) cannot be written in the form of p/q so it is a irrational No

Answer 2

Answer:

let assume √3 is irrational

Step-by-step explanation:

√3=a/b[where a and b are co -prime numbers]

b√3=a

by squaring both sides

3b²=a²-[1]

∴ a divides by 3

let a =3c where c is an integer

put in equation [1]

3b²=[3c²]

3b²=9c²

3b²/9=c²

b²/3=c²-[2]

this means 3 divides b

therefore from equation [1] and [2] we have 3 is least common factor of a and b .

but this contradiction the fact a and b have common factor . so our assumption is wrong .

∴√3 is  irrational number.

if my answer is helpful for you please click on rating or thanks