Question

prove √2 is not rational number plz

Answer 1

If you write root 2 in decimal form you will find that is in non repeating and non terminating which are the properties of irrational number and that is why it is irrational

Answer 2

first let us assume that √2 is a rational no
so it can b expressed in the form of p/q
√2=p/q
squaring both sides
after squaring both sides we get
2 =p^2/q^2
2q^2=p^2 (equation 1)
now 2 divides p^2
so 2 will divide p also (its a theorem)
now
let us take
p=2m
after squaring
p^2=4m^2(equation2)
putting eq2 in eq1
2q^2=4m^2
q^2=2m^2
now 2 divides q^2
so 2 will divide q also
we get a common factor of p and q and i.e.2
it proves that our assumption is wrong
hence √2 is a irr....no
I no its a big process but don't get confuse it is easy and still if u have any confusion u can ask me
I hope it hlps