Question

pls prove root 7 is an irrational no. pls tell........

Answer 1

•Let us assume that √7 is rational number.

•√7=p/q.(where p and q are co primes and q is not equal to zero).

•Squaring on both sides.

•We get ,

•7=p^2/q^2

•p^2=7q^2......(i)

•Here 7 divides p^2

•Therefore, 7divides p.

•So we can say that 7 is a factor of p.

•p/7=c

•Squaring on both sides

•p^2/49=c^2

•p^2=49c^2.......(ii)

•From (i) and (ii)

•We get,

•49c^2=7q^2

•7c^2=q^2

•Here 7divides q^2

•Therefore, 7 divides q.

•So 7 is a factor of q.

•Here 7 is factor of both p and q but p and q are Co primes.

•Hence our assumption is wrong.

•Therefore, we can say that √7 is irrational number.

Hope it helps u.!!!!!