Question

How to prove that a number is irrational?

Answer 1

let the number be 5-√3

first we have to assume the given number as rational number

then we have to write that number as 5-√3=p/q

and assume the both p and q as integers which have no common factor except 1

then after solving we will get 5-p/q=√3

then√3= 5q-p/q

then 5q-p/q is proved as rational no. which have p and q as integers

√3 is also a rational number which is a contradiction

Thus assumption is wrong

hence,5-√3 is an irrational number

We have to keep those steps in mind to prove a given number as irrational number.