Question

show that √n is irrational if n is prime or not a perfect square​

Answer 1

Answer:

if a number is prime it doesnt have any factor other than itself so whenever u divide it by numerator answer will be non recurring and non repeating which means it is irrational

Step-by-step explanation:

Answer 2

let n be rational no.
such that
r=a/b
squaring both the sides
r2=a2/b2....(1)
i,e a2 is divisible by 2
so a be aslo divisible by 2
that a=c/2
putting value of a in eq. 1
4c/b2=r2
r=2c/b
i,e
b2 is alo divisible by 2
so b be also divided by 2
but this contradict the fact that it is coprime
so our assumption is wrong
so root n is irration no.