Question

prove (2route 3)/5 is a irrational numbers

Answer 1

to prove: (2 root 3 )/5 is irrational numbers
proof :let (2 root 3)/5 is a rational number.
so,(2root 3)/5is in the form of p/q .
if 2root3 is rational then root3 is also rational.
taking root3
we get,
root3=P/q
on squaring both side ,
3=p^2/q^2
3p^2=q^2-------------(1)
s
3 divide q^2
3 also divide q
again,
3q^2=p^2
3divide p^2 -------(2)
3divisio q
from equation (1)and (2)
we get
3 is not in the form of p/q
hence our exemption is wrong
hence it is proved that (2root3)/5 is irrational.