Question

prove by induction: sqrt(2) is irrational.

Answer 1

sqr2=1.4142135623730950... it can't b written as a ratio of 2 no.s :P:P

Answer 2

1<2<4
so,1<sqrt2<2
so,sqrt2 is not an integer.
suppose,it is rational.
then,sqrt2=p/q (p & q are integers & prime to each other)
or,2=p^2/q^2
or,2q=p^2/q
now,2q is an integer,but ( p^2/q) is not,as p & q are prime to each other.
so,L.H.S=integer but R.H.S is not.so,sqrt2 cant be rational