Question

prove that root7 is irrational​

Answer 1

√7=2.6457513110645

non terminating..

so it is irrational number..

hence proved

Answer 2

Step-by-step explanation:

Lets assume √7 is rational number i.e. √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 having no common factor

√7= a/b co-prime number

√7=a/b

a=√7b

squaring

a^2=7b^2 ......1

a^2 is divisible by 7

a=7c

substituting values in 1

(7c)^2=7b^2

49c^2=7b^2

7c^2=b^2

b^2=7c^2

b^2 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 bcoz of our wrong assumption.

√7 is irrational.

Hope it is helpful!

Thanks