document.write( "Question 964707: Assume that both sqrt(x) and sqrt(y) are simplified completely and that ≠ .
\n" ); document.write( "Why is it always possible to multiply sqrt(x)and sqrt(y) together and get sqrt(xy) for the product, but not always possible to add sqrt(x) and sqrt(y) together and get sqrt(x+y)
\n" ); document.write( "for the sum?
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Algebra.Com's Answer #589525 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Because,
\n" ); document.write( " $\"sqrt%28x%29%2Asqrt%28y%29=sqrt%28xy%29\"$
\n" ); document.write( "but
\n" ); document.write( " $\"sqrt%28x%29%2Bsqrt%28y%29%3C%3Esqrt%28x%2By%29\"$
\n" ); document.write( ".
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\n" ); document.write( "Let's assume it did,
\n" ); document.write( " $\"sqrt%28x%29%2Bsqrt%28y%29=sqrt%28x%2By%29\"$
\n" ); document.write( "Square both sides,
\n" ); document.write( " $\"%28sqrt%28x%29%2Bsqrt%28y%29%29%5E2=x%2By\"$
\n" ); document.write( " $\"sqrt%28x%29sqrt%28x%29%2B2sqrt%28x%29sqrt%28y%29%2Bsqrt%28y%29sqrt%28y%29=x%2By\"$
\n" ); document.write( " $\"x%2B2sqrt%28xy%29%2By=x%2By\"$
\n" ); document.write( " $\"2sqrt%28xy%29=0\"$
\n" ); document.write( "The left side is only equal to the right when $\"x=0\"$ or $\"y=0\"$ or $\"x=y=0\"$ .
\n" ); document.write( "So it's not an identity, so,
\n" ); document.write( " $\"sqrt%28x%29%2Bsqrt%28y%29%3C%3Esqrt%28x%2By%29\"$
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