document.write( "Question 290438: Is it always true that √(a^2+b^2 )=a+b? Is it sometimes true? Or is it always false? Please use and example. \n" ); document.write( "

Algebra.Com's Answer #210166 by toidayma(44) $\"\"$ $\"About$

You can put this solution on YOUR website!
You can answer the question by finding the condition of a,b so that:
\n" ); document.write( " $\"sqrt%28a%5E2+%2B+b%5E2%29+=+a+%2B+b\"$
\n" ); document.write( "- The first condition is that (a+b) >= 0 since the left side of the equation is never negative.
\n" ); document.write( "- When both sides are both >= 0, we have:
\n" ); document.write( " $\"sqrt%28a%5E2+%2B+b%5E2%29+=+a+%2B+b\"$ <-> $\"a%5E2+%2B+b%5E2+=+%28a%2Bb%29%5E2\"$ <-> 2*a*b = 0 <-> a = 0 or b = 0.\r
\n" ); document.write( "\n" ); document.write( "Therefore, (1) is true with two conditions: (1) a + b >= 0 and (2) a*b = 0.
\n" ); document.write( "Is it clear now? \n" ); document.write( "

\n" );