Question

prove that root 3 is an irrational number

Answer 1

we should prove it by taking a contrary way.let root 3 be rational.a rational number will be in the form of p/q.so,root 3=p/qhere p and q are in simplified form.so,they are co-primes,whose H.C.F. is 1.so,1 is a factor of root 3.
root 3=p/qp=q*root3squaring on both sidesp^2=3q^2