Question 67496
<pre><font size = 4><b>please help 

{{{ sqrt(75t^3)+8sqrt(108t^3) }}}

Break everything down into prime factors with
no exponents showing:


{{{ sqrt(3*5*5*t*t*t)+8sqrt(2*2*3*3*3*t*t*t) }}}

Since it's a square root, pair up groups of two
(pairs) of like factors:


{{{ sqrt(3*(5*5)*(t*t)*t)+8sqrt((2*2)*(3*3)*3*(t*t)*t) }}}

The pair of 5's and the pair of t's under the first radical
come out front as a single 5 and a single t, the 3 and the
t that did not pair up stay under the radical:


{{{ 5*t*sqrt(3*t)+8sqrt((2*2)*(3*3)*3*(t*t)*t) }}}

The pair of 2's, the pair of 3's, and the pair of t's under
the second radical come out front as a single 2, a single 3,
and a single t, the 3 and the t that did not pair up stay 
under the radical:

      {{{ 5*t*sqrt(3*t)+8*2*3*t*sqrt(3*t) }}}

      {{{ 5t*sqrt(3t)+48t*sqrt(3t) }}}

Factor out {{{t*sqrt(3t)}}}

      {{{ t*sqrt(3t)}}}{{{(5 + 48)}}}

      {{{ t*sqrt(3t)}}}{{{(53)}}}

      {{{ 53t*sqrt(3t)}}}

Edwin</pre>