Question 447774
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how to simplify sqrt (12ab^3c^2)
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        The answer    {{{2bc*sqrt(3ab)}}}    in the post by @mananth is  {{{highlight(highlight(INCORRECT))}}}.


        The correct answer is    {{{2*abs(b)*abs(c)*sqrt(3*a*b)}}}.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>E x p l a n a t i o n</U>



<pre>
In problems of this kind, we assume that the variables are real numbers and the expression under the square root
is non-negative.


We should understand that c^2 is necessary (always) non-negative, but 'c' itself can be negative.


We also should understand that  ' b '  can be negative (together with b^3), but the product ' a*b^3 '  is necessary non-negative,
same as the product  ' ab '.


In the problems of this kind, it is also assumed that the value of the square root itself is also non-negative.


Therefore, when ' b^2 ' goes out the square root, it comes to outside as |b|, the absolute value of  ' b '.


Similarly, when ' c^2 ' goes out the square root, it comes to outside as |c|, the absolute value of  ' c '.


Therefore, the final formula in the answer is as it is shown in my post at the beginning.
</pre>

Solved correctly and explained completely.