Question

Please help me friends pleass prove that √7 is irrational.

Answer 1

Answer:

hope you will understand it

Answer 2

suppose √7 is a rational number

√7=a/b, a and b are coprime numbers

√7=a/b

squareing both sides

7=a2/b2

7b2=a2

therefore,7 divides a2

so, also 7 divides a.

so, we can write a=7c for some integer c.

substitute for a, we get 7b2=49c2

b2=7c2

2 divides b2

also 2 divides b

therefore , a and b have atleast 7 as a common factor.

but, it is contradiction fact that a and b are coprime numbers.

this contradiction arise because of our wrong assumption

so √7 is irrational number .