document.write( "Question 150807: Please help with this problem.
\n" ); document.write( "Z=sqrt((1000^2)+(1592^2))
\n" ); document.write( "It is my understanding that the square root of a \"number\" squared is the \"number\".
\n" ); document.write( "If this is true I would solve this as: Z=1000+1592 so Z=2592, but Im not sure this is correct \n" ); document.write( "

Algebra.Com's Answer #110732 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Evaluate:
\n" ); document.write( " $\"Z+=+sqrt%28%281000%5E2%29%2B%281592%5E2%29%29\"$
\n" ); document.write( "While your statement - \"...the square root of a 'number' squared is the 'number'.\" is true, your conclusion is faulty.
\n" ); document.write( "You can easily see this in the Pytagorean theorem:
\n" ); document.write( " $\"c%5E2+=+a%5E2%2Bb%5E2\"$ Taking the square root of both sides we get...
\n" ); document.write( " $\"c+=+sqrt%28a%5E2%2Bb%5E2%29\"$ and this is NOT the same as $\"c+=+a%2Bb\"$ because the sum of the squares is not the same as the sum of the numbers, so...
\n" ); document.write( " $\"Z+=+sqrt%28%281000%5E2%29%2B%281592%5E2%29%29\"$ Square the numbers under the radical sign.
\n" ); document.write( " $\"Z+=+sqrt%281000000%2B2534464%29\"$ Add the numbers under the radical sign.
\n" ); document.write( " $\"Z+=+sqrt%283534464%29\"$ Now extract the square root.
\n" ); document.write( " $\"Z+=+1880.017\"$ ...and this is an irrational number (a non-repeating, non-terminating decimal). \n" ); document.write( "

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