Question

prove that √5 is an irrational number.

Answer 1

prove √5 is rational


√5= where p and q are coprime

P = √5q
Squaring both sides

P2 = (√5q)2
P2 = 5q2 -----------------(1)


So, p = 5r --------------(2)


Putting value of eq. (2) in (1) we get,
25r2 = 5q2


dividing from 5 on both sides we get,

= 5r2 = q2


So, √5 is irrational.

Answer 2

let root 5 be a rational
then it must be in p/q form where q not = to 0 and p &q are co-prime .
root 5= p/q
=>root 5 *q = p
squaring on both the sides
=>5*q*q = p*p --->1
p*p is divisible by 5
p is divisible by 5
p= 5 c ( c is a positive integer )
-squaring on both the sides
p*p = 25 c*c ---->2
sub p*p in 1
5*q*q= 25 c*c
q*q =5*c*c
=>q is diviible by 5
thus q and p have a common factor 5
there is a contradiction
as our assumption p&q are co-prome it has a common factor
so root 5 is an irrational
hiya...I jst understood this frm net and answered..hope it helps