Question 693928
I believe that you meant {{{(9 +- sqrt(693))/3}}} which you could write as (9 +- sqrt(693))/3.
Since the digits of {{{693}}} add to {{{18}}}, which is a multiple of {{{9}}},
we know that {{{693}}} is a multiple of {{{9}}},
so we divide to find {{{693/9=77}}} <--> {{{693=9*77}}}.
We also know that {{{sqrt(9)=3}}}.
We also know that {{{9=3*3}}}.
So,
{{{(9 +- sqrt(693))/3=(3*3 +- sqrt(9*77))/3=(3*3 +- sqrt(9)*sqrt(77))/3=(3*3 +- 3sqrt(77))/3=3(3+-sqrt(77))/3=highlight(3+-sqrt(77))}}}
 
(If you meant 9 +- sqrt(693)/3 = {{{9 +- sqrt(693)}}}/{{{3}}} = {{{9 +- sqrt(693)/3}}}, which is a different number, I am sorry to have misinterpreted).