Question

Prove that under root 5 is an irrational number very urgent

Answer 1

let under root 5 is a rational no
under root 5=a/b(a and b are co prime hcf=1)
squaring on both sides
5=araise to power 2/braise to power 2
b raise to power 2=a raise to power 2/5 name it eq 1
it means 5 divides a raise to power 2
it means 5 divides a also
a=5m name it eq 2
put value of eq 2 in 1
b raise to power 2=5mraise to power 2/5
b raise to power 2 =25 mraise power 2/5
b raise to power 2=5m raise to power2
b raise to power 2/5=mraise to power 2
it means 5 divides b raise to power 2
it means 5 divides b also
hence,5 is common factor of both a and b so it is contradiction therefore,suposition is wrong so under root 5is irrational

Answer 2

hey dude here is your answer...

first let you know....

irrational numbers are those which cannot be return in the form of p and q

let √5=p/q

sq.both sides
(√5)²=(p/q)²
p²=5q²+0--------1
5/p²
5/p

let p=5m
from--1 (5m) ²=5q²
25m²=5q²
q²=5m²
5/q²
5/q

5 is a irrational number of p and q

hope this will help you