Question 886736
<pre>
Break those numbers down into prime factors using factor trees:

{{{matrix(1,5,3sqrt(726),""+"",4sqrt(252),""-"",8sqrt(63))}}}

     726               252                 63
     / \               / \                 /\
    2  263            2  126              9  7 
       / \               / \             / \   
      3  121            2  63           3   3
         / \               /\ 
        11 11             7  9 
                            / \
                           3   3

726 = 2·3·11²,     252 = 2²·3²·7       63 = 3²·7

{{{matrix(1,5,3sqrt(2*3*11^2),""+"",4sqrt(2^2*3^2*7),""-"",8sqrt(3^2*7))}}}

Take all the numbers with squares out from under the radical and place
the numbers without the squares out in front of the radicals:

{{{11^2}}} comes out of the first radical as a 11 muiltiplied in front.
Both {{{2^2}}} and {{{3^2}}} come out from under the radical in the second
radical, as a 2 multiplied by a 3 in front of the second radical:

{{{matrix(1,5,3*11*sqrt(2*3),""+"",4*2*3*sqrt(7),""-"",8*3*sqrt(7))}}}

{{{matrix(1,5,33*sqrt(6),""+"",24*sqrt(7),""-"",24*sqrt(7))}}}

The 2nd and 3rd terms cancel and you're only left with the fitst term:

{{{33*sqrt(6)}}}

Edwin</pre>