<PRE><B>Question 969387</B>
&lt;br&gt;
Consider this:&lt;br&gt;
{{{(sqrt(x)+sqrt(y))^2=(x+y)+2sqrt(xy)}}}&lt;br&gt;
In the form on the right, the rational part is the sum of two integers and the expression under the radical is the product of those two integers, and there is a multiplier &quot;2&quot; outside the radical.&lt;br&gt;
In your problem, you are to find&lt;br&gt;
{{{sqrt(5*2sqrt(6))}}}&lt;br&gt;
This is in the form of the pattern above: 5 is the sum of 2 and 3; 6 is the product of 2 and 3; and the radical has a multiplier &quot;2&quot;.  So the problem fits the pattern:&lt;br&gt;
{{{sqrt(5+2sqrt(6))=sqrt(3)+sqrt(2)}}}&lt;br&gt;
Here are a couple of random examples to help you see the pattern:&lt;br&gt;
{{{sqrt(17+2sqrt(70))=sqrt(10)+sqrt(7)}}} [17 is 10+7; 70 is 10*7]&lt;br&gt;
{{{sqrt(9+2sqrt(14))=sqrt(7)+sqrt(2)}}} [9 is 7+2; 14 is 7*2]&lt;br&gt;
ANSWER: {{{sqrt(5+2sqrt(6))=sqrt(3)+sqrt(2)}}}&lt;br&gt;
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