Question

show √3 is a irrational.

Answer 1

hey dear


here is your answer


Solution


Let us assume to the contrary that √3 is rational

Then we can find integers a and b ( unequal to 0)

such that -

√3 = a / b


suppose a and b have common factors other than 1

then we can divide common factor and

assume that a and b are Co prime

So,

b√3 = a

square on both sides

and rearrange them we get

3b^2 = a^2


Therefore a^2 is divisible by 3


so we can write a = 3c for some integer c

substituting for a we get 3b^2 =9c^2


that is b^2 = 3c^2


This means that b^2 is divisible by 3 with p= 3


therefore a and b have at least 3 as common factor



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


therefore √3 is irrational number


hence proved


hope it helps

thank you

Answer 2

Hope this will help you!!!