document.write( "Question 399498: sqrt (a+2)^2 \n" ); document.write( "

Algebra.Com's Answer #282892 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Is it
\n" ); document.write( " $\"sqrt%28%28a%2B2%29%5E2%29\"$
\n" ); document.write( "or
\n" ); document.write( " $\"%28sqrt%28a%2B2%29%29%5E2\"$ ?
\n" ); document.write( "It makes a difference. In the first expression we do not know if (a+2) is positive or negative. In the second expression, since a+2 is inside of a square root, we know that a+2 cannot be negative.

\n" ); document.write( "Both of these expressions look like they would simplify to a+2. But square roots are supposed to be positive (or zero). With the first expression, since we do not if a+2 is positive we must use absolute value to ensure that we have a positive (or zero) result.
\n" ); document.write( " $\"sqrt%28%28a%2B2%29%5E2%29+=+abs%28a%2B2%29\"$

\n" ); document.write( "With the second expression, since we know that a+2 cannot be negative, we do not need absolute value:
\n" ); document.write( " $\"%28sqrt%28a%2B2%29%29%5E2+=+a%2B2\"$
\n" ); document.write( " \n" ); document.write( "

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