document.write( "Question 72584: is the suare root of x^2 = x an identity (true for all values of x) explain? \n" ); document.write( "

Algebra.Com's Answer #52042 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
\n" ); document.write( " $\"sqrt%284%29\"$ equals plus or minus 2 (we need to have both). Since the absolute value of both a positive and a negative number is positive, the absolute value can be used in this case.
\n" ); document.write( " $\"abs%28x%29=a\"$
\n" ); document.write( " $\"x=0%2B-a\"$ This is why $\"abs%28x%29\"$ is used in the identity instead of x (ignore the 0). \n" ); document.write( "

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