Root 7 is irrational prove it
Answers
HOPE YOU ARE HELPED. . . . .
let us suppose root 7 is rational number
where,root 7 = p/q and p and q both are integers , q is not equals to 0
and they r co prime...
root 7 = p/q
q√7 = p .....(i)
squaring both sides...
(q√7)^2 = p^2
7q^2 = p^2
q^2 = p^2/7
we know if 7 divides p^2 then it also divides p...
p is divided by 7 .....(A)
let , p = 7r
put in (i).....
q√7 = 7r
squaring both sides...
(q√7)^2 = (7r)^2
7q^2 = 49r^2
q^2 = 49r^2/7
q^2 = 7r^2
q^2/7 = r^2
similarly, if 7 divides q^2 then it also divides q.....
q is divisible by 7......(B)
from the above observations (A)and(B)...
we can say that p and q both are divisible by 7 and this contradicts the fact that p and q are co prime ...
hence , our supposition was wrong that √7 is rational number.....
hence, √7 is irrational.........