Question

plz solve my question to detail

Answer 1

let us assume , to the contray that 7√3 is irrational
that is  we can find integers a and b (not = to 0 ) such that 7√3 = a/b

=> 7b√3=a
=> 21b²= a² 
=> therefore a divides 21

we can write a=21c
substituting a we get 21b²=441c²
hence b divides 21

then this contradicts the fact that 7√3 is rational 
therefore we get to know 7√3 is irrational