Question

Prove that root 7 is an irrational number.

Answer 1

Lets assume that √7 is rational number. ie √7=p/q. suppose p/q have common factor then we divide by the common factor to get √7 = a/b were a and b are co-prime number. that is a and b have no common factor. √7 =a/b co- prime number √7= a/b a=√7b squaring a²=7b² .......1 a² is divisible by 7 a=7c substituting values in 1 (7c)²=7b² 49c²=7b² 7c²=b² b²=7c² b² is divisible by 7 that is a and b have atleast one common factor 7. This is contridite to the fact that a and b have no common factor.This is happen because of our wrong assumption. √7 is irrational

Answer 2

Answer:

Lets assume that √7 is rational number. ie √7=p/q.

suppose p/q have common factor then

we divide by the common factor to get √7 = a/b were a and b are co-prime number.

that is a and b have no common factor.

√7 =a/b co- prime number

√7= a/b

a=√7b

squaring

a²=7b² .......1

a² is divisible by 7

a=7c

substituting values in 1

(7c)²=7b²

49c²=7b²

7c²=b²

b²=7c²

b² is divisible by 7

that is a and b have atleast one common factor 7. This is contridite to the fact that a and b have no common factor.This is happen because of our wrong assumption.

√7 is irrational