document.write( "Question 238428: What is wrong with the following? √25 = ą5 \n" ); document.write( "

Algebra.Com's Answer #175185 by jsmallt9(3758) $\"\"$ $\"About$

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$\"sqrt%2825%29+=+5\"$ In fact the square root of any number is positive.

\n" ); document.write( "The \"+-\" you sometimes see in connection with square roots comes from solving equations like:
\n" ); document.write( " $\"x%5E2+=+25\"$
\n" ); document.write( "Find the square root of each side:
\n" ); document.write( " $\"sqrt%28x%5E2%29+=+sqrt%2825%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"abs%28x%29+=+5\"$
\n" ); document.write( "We cannot say $\"sqrt%28x%5E2%29=+x\"$ . x may not be positive and all square roots are positive. This last step is often skipped and this leads to the confusion. It is the solution to the absolute value equation which gives us the \"+-\", not the square roots.:
\n" ); document.write( "x = +-5 \n" ); document.write( "

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