Question 792441
<pre>
-6&#8730;<span style="text-decoration: overline">63</span> - 9&#8730;<span style="text-decoration: overline">28</span> + 2&#8730;<span style="text-decoration: overline">14</span>

Factor 63 as 9*7 and then as 3²·7, so 63 contains a perfect square factor

Factor 28 as 4*7 and then as 2²·7, so 28 contains a perfect square factor

Factor 14 as 2*7 but 14 does not contains a perfect square factor,
so we just leave it as 14

-6&#8730;<span style="text-decoration: overline">3²·7</span> - 9&#8730;<span style="text-decoration: overline">2²·7</span> + 2&#8730;<span style="text-decoration: overline">14</span>

We can take 3² out of the first square root as 3 
in front and take 2² out of the second square root 
as 2 in front, like this:

-6·3&#8730;<span style="text-decoration: overline">7</span> - 9·2&#8730;<span style="text-decoration: overline">7</span> + 2&#8730;<span style="text-decoration: overline">14</span>

-18&#8730;<span style="text-decoration: overline">7</span> - 18&#8730;<span style="text-decoration: overline">7</span> + 2&#8730;<span style="text-decoration: overline">14</span>

The first two terms combine as -36&#8730;<span style="text-decoration: overline">7</span>

-36&#8730;<span style="text-decoration: overline">7</span> + 2&#8730;<span style="text-decoration: overline">14</span>

That's the simplest radical form.

Edwin</pre>