Question

prove root 7 is irrational number

Answer 1

√7 can not be expressed as p/q where p & q are both natural number & co prime number

Answer 2

Let assume on the contrary that ✓7 is rational no.
(✓7)^2 = (a/b)^2
7= a^2/b^2
a^2= 7b^2. ...(1)
a^2 is the multiple of 7
a is the multiple of 7
a=7c for some integer c
a^2 =49c^2
7b^2=49c^2
b^2=7c^2
b^2 is the multiple of 7
b is the multiple of 7. ....(2)
From (1) and (2) have a least 7 as a common factor . But this contradicts the fact that a and b are co prime this means that ✓7 is an irrational number