document.write( "Question 73010: Is sqrt x^2=x an identity (true for all values of x)?
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\n" ); document.write( "\n" ); document.write( "Explain your answer in this space.
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Algebra.Com's Answer #52241 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
No it is not, well maybe if you were more precise and said
\n" ); document.write( " $\"sqrt%28x%5E2%29=abs%28x%29\"$ is an identity, you would be right(The bars show absolute value)
\n" ); document.write( "The simple reason why (there are more complicated versions which have their purpose) is because when you take the square root of any number you get 2 answers. For instance, lets say you have
\n" ); document.write( " $\"x%5E2=a\"$
\n" ); document.write( "We cannot say the $\"x=sqrt%28a%29\"$ is true since there are two answers. This is the true answer
\n" ); document.write( " $\"x=0%2B-sqrt%28a%29\"$ Since there are 2 answers (ignore the zero)
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\n" ); document.write( "The same idea applies in this case; however, instead of using the plus or minus, we go for the absolute value since it represents the distance positive and negative numbers are from zero on the number line. In other words, since
\n" ); document.write( " $\"abs%28x%29=a\"$
\n" ); document.write( " $\"x=0%2B-a\"$ (in other words, x is both positive and negative)
\n" ); document.write( " $\"0%2B-sqrt%28x%5E2%29=x\"$ Now we can from this
\n" ); document.write( " $\"sqrt%28x%5E2%29=abs%28x%29\"$ To this, which is an identity.
\n" ); document.write( "Hope that makes sense. Feel free to ask questions if you are lost. \n" ); document.write( "

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