Question

prove $\sqrt{5}$ to be irrational

Answer 1

we will do it by contradiction.

let √5 be a rational no. in form a/b which is in simplest form

therefore

a/b=√5

squaring both sides

a^2=5b^2

by prime number thereom if p divides a square it divides a as well

therefore we can write a=5c

substituting this in previous equation we get b^2=5c^2

therefore a and b have one factor that is 5 in common.

therefore it contradicts previous statement that root 5 is rational in form a and b which is in simplest form.