document.write( "Question 356824: Is sqrt(x^2) = x for every real number x? Please explain your reasoning. \n" ); document.write( "
Algebra.Com's Answer #254772 by CharlesG2(834)\"\" \"About 
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Is sqrt(x^2) = x for every real number x? Please explain your reasoning. \r
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\n" ); document.write( "\n" ); document.write( "x = -3, x^2 = 9, sqrt(x^2) = 3 or -3 since both squared equal 9
\n" ); document.write( "x = 0, x^2 = 0, sqrt(x^2) = 0, 0 is not positive or negative
\n" ); document.write( "x = 3, x^2 = 9, sqrt(x^2) = 3 or -3 since both squared equal 9\r
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\n" ); document.write( "\n" ); document.write( "the principal square root is the positive root not the negative one\r
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\n" ); document.write( "\n" ); document.write( "if you only looking for principal square roots, sqrt(x^2) = x is a one square to one root relationship\r
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\n" ); document.write( "\n" ); document.write( "if you not just looking for principal square roots, sqrt(x^2) = x is a one square to two roots relationship\r
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\n" ); document.write( "\n" ); document.write( "sqrt(x^2) = x, unless you looking for principal values of x has two values of x that will make the equation work, the positive value and the negative value, unless x = 0\r
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\n" ); document.write( "\n" ); document.write( "So does sqrt(x^2) = x for every real number x?
\n" ); document.write( "Yes if x is the principal root of x^2.
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