Question

prove root 5 is an irrational by using long division method

Answer 1

let √5 be a rational no
thus. √5=p/q. (where p,q are co-prime ; € Z and q is not equal to zero)

p=√5q. (sq both sides )
p^2= 5q^2. (i)

p^2 is divisible by 5
p is divisible by 5

now,
let p=5r. (sq both sides)
p^2=25r^2. (ii)

p^2 is divisible by 25

from (i) &(ii)
5q^2=25r^2
q^2=5r^2

q^2 is divisible by 5
q is divisible by 5

but p and q are co-prime no's
therefore our assumption is wrong
this, √5 is an irrational no

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