Question 972558
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how do you simplify radical 8x squared
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        @lwsshak3 gives the answer in his post {{{2x*sqrt(2)}}}.


        This answer is incorrect, and I will explain it below.



In expression  {{{sqrt(8x^2)}}},  value of x can be positive or negative (or zero).


Expression  {{{sqrt(8x^2)}}}  makes sense and is defined for both positive and/or negative values of x.


Also, according to the common agreement, square root of a number is understood in a middle school as a positive value.


THEREFORE,  the correct answer to the problem's question is   {{{2*abs(x)*sqrt(2)}}}.


It works universally for positive and negative values of  'x',

while expression  {{{2x*sqrt(2)}}}  gives a negative value for negative  'x',  which contradicts to the common agreement.


This question/problem is a standard  {{{highlight(highlight(TRAP))}}},  and almost all 
unfortunate newcomers, who are not familiar with this explanation,  fall into this trap.



The percentage of these unfortunate newcomers is about  99.999%,  I think,  or even more than that.