Question 135825
So your problem looks like this:  {{{sqrt(75)/sqrt(3)}}}.


The reason that this assignment is called simplifying radical expressions is that the square root sign is called a radical.


Quotient of two radicals rule:


{{{root(n,a)/root(n,b)=root(n,a/b)}}} so long as when n is even, {{{a>=0}}} and {{{b>0}}} or when n is odd {{{b<>0}}}


Since n is understood to be 2 when not specified, let's check our numbers:


{{{75>=0}}}: True
{{{3>0}}}: True


That means we can apply the rule, so:


{{{sqrt(75)/sqrt(3)=sqrt(75/3)=sqrt(25)=5}}}.