Question 77916
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1.   {{{sqrt(50)}}}

   = {{{sqrt(10*5)}}} <---- should be {{{sqrt(25*2)}}}
   = {{{sqrt(10)*(5)}}} <--- should be {{{sqrt(25)* sqrt(2)}}}
   = {{{5*sqrt(5)}}} <--- should be {{{5*sqrt(2)}}}

The thing to do is to begin by looking at 50 and trying to find some factor or factors
that are squares.  In this case 25 is a factor of 50 that has a "nice" square root of 5.
The comments after the <---- show you the way to simplify the problem step by step and the
answer to this problem is {{{5*sqrt(2)}}}
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2.   {{{sqrt(72x^3)}}}
   ={{{9*x^2*8x}}}<---- the biggest factor of 72 that is a square is 36. Use {{{36x^2*2x}}}
This converts the problem to {{{sqrt(36*x^2)*sqrt(2*x)}}}
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={{{3x*sqrt(8x) =3x*sqrt(2x)}}} <---- should be {{{6x*sqrt(2x)}}}
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You had the right idea here.  Your last step almost got the correct answer.  Your last 
step should have been:
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={{{3x*sqrt(8x)=3x*sqrt(4*2x) = 3x*sqrt(4)*sqrt(2x)= 3x*2*sqrt(2x) = 6x*sqrt(2x)}}}
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and this is the correct answer.
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Hope this gives you a little more insight to the problem. You seem to have the basic idea
of solving problems such as these and just needed a couple of minor suggestions to get you
back on track. Keep up the good work.