Question

classify the following nuber as irrational : ✓225

Answer 1

it is a rational no. as 225 is squre of 15 so it can be written in form ofp/q

Answer 2

assume root 225 is rational
then it can be in the form of
root225:-p/q then
root225 *q :- p
squaring on both side
(root225) square * q square :- p. square
then
225. * q square :- p. square. (1)
by therom
225. is factor of p. square.
and also
225. is factor of p. then
225/ p square
225/ p
let 225*a square :- p
225 *q square :- 225 square * a square
q square :- 225 * a square
therefore
225 is a factor q square
and
225 is a factor q. therefore. (2)
from 1 & 2
we can say that root225 is irrational.



but root 225 also can be writing in the form of root 15*15 then
15 will remain
but 15 is rational
so
question. is wrong