Question 477556
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A square has an area of x^2 + 6x + 9. Find the length of a side. Make a sketch of the square Please help
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        Tutor @Theo' solution is many words.


        I  don't like toooo wordy solutions: I think that too wordy explanations are bad style to teach Math.  

        So, I will write another solution, much shorter and, I believe, more educative.



<pre>
The expression  x^2 + 6x + 9  represents an algebraic perfect square  {{{(x+3)^2}}}.

        So, the area of the square is  {{{(x+3)^2}}}  square units.


Hence, the side length of this square is square root of this perfect square {{{(x+3)^2}}}.


So, our first desire is to declare that the side length is  (x+3)  units.


But it would be too hastily and not always correct.


The reason is that this expression (x+3) can be negative, since we don't know what 'x' is.


Meanwhile, the length of the square must be positive due to the meaning of this notion/conception.


Therefore, more accurate is to write  {{{sqrt((x+3)^2)}}} = |x+3| ,  using the absolute value.


This form is universally correct for all possible values of 'x'.


<U>ANSWER</U>.  If the area of a square is  x^2 + 6x + 9  square units,  then the side of the square is  |x+3|  units.
</pre>

Solved, with complete explanations in compact form.