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how to simplify sqrt (12ab^3c^2)
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The answer 
in the post by @mananth is 
.
The correct answer is 
.
E x p l a n a t i o n
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.
Solved correctly and explained completely.
