Question

prove the√7 is a irrational numbers​

Answer 1

Step-by-step explanation:

root 7 is irrational number becoz they don't have common factor other than one and seven

Answer 2

Step-by-step explanation:

let , root 7 = a/ b ( where a and b are co prime integers and b is not equal to 0 )

root 7× b = a

sbs: 7b^2 = a^2 (1)

hence , 7 is a factor of a (2)

so, a = 7c

put value of a in eq. 1

7b^2 = (7c)²

b² = 7c

hence , 7 is a factor of b (3)

from eq. 1 and 2

7 is a common factor of a and b

but this contradicts the fact that a and b are co prime

Therefore , root 7 is irrational