Question 1152514
.
<pre>

The key step is to notice (or to derive) that


    32 - {{{6*sqrt(15)}}} = {{{(3*sqrt(3) - sqrt(5))^2}}}.    (1)


Indeed, square the binomial  {{{3*sqrt(3) - sqrt(5)}}},  using the formula   {{{(a-b)^2}}} = {{{a^2 - 2ab + b^2}}}  with a = {{{3*sqrt(3)}}}  and  b = {{{sqrt(5)}}}.


As soon as you established it, only one step remained to the answer:


    the square root of  {{{32-6*sqrt(15)}}} is the square root of the right side of (1),  which (i.e. the square root)  is  {{{3*sqrt(3) - sqrt(5)}}}.    <U>ANSWER</U>
</pre>