document.write( "Question 373662: Simplify the following expression.
\n" ); document.write( "\"sqrt+%28-98%29+sqrt+%28-50%29+\" \n" ); document.write( "
Algebra.Com's Answer #265922 by jsmallt9(3758)\"\" \"About 
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\"sqrt%28-98%29%2Asqrt%28-50%29\"
\n" ); document.write( "Since we have negative radicands (expressions within a radical) of an even numbered root (square roots are 2nd roots), we start by factoring out -1:
\n" ); document.write( "\"sqrt%28-1%2A98%29%2Asqrt%28-1%2A50%29\"
\n" ); document.write( "Then we use a property of radicals, \"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\", to separate the -1 factors into their own square roots:
\n" ); document.write( "\"sqrt%28-1%29%2Asqrt%2898%29%2Asqrt%28-1%29%2Asqrt%2850%29\"
\n" ); document.write( "Since \"sqrt%28-1%29+=+i\" this becomes:
\n" ); document.write( "\"i%2Asqrt%2898%29%2Ai%2Asqrt%2850%29\"
\n" ); document.write( "We could multiply out the remaining square roots. But instead of multiply 98*50, I am going to simplify the square roots before I multiply them:
\n" ); document.write( "\"i%2Asqrt%2849%2A2%29%2Ai%2Asqrt%2825%2A2%29\"
\n" ); document.write( "\"i%2Asqrt%2849%29%2Asqrt%282%29%2Ai%2Asqrt%2825%29%2Asqrt%282%29\"
\n" ); document.write( "Since \"sqrt%2849%29+=+7\" and \"sqrt%2825%29+=+5\" this becomes:
\n" ); document.write( "\"i%2A7%2Asqrt%282%29%2Ai%2A5%2Asqrt%282%29\"
\n" ); document.write( "Since this is all multiplication, the Commutative and Associative Properties apply. So we can rearrange the order and rearrange the grouping in any ways we choose:
\n" ); document.write( "\"7%2A5%2A%28sqrt%282%29%2Asqrt%282%29%29%2A%28i%2Ai%29\"
\n" ); document.write( "Since \"sqrt%282%29%2Asqrt%282%29+=+2\" (by definition), this becomes:
\n" ); document.write( "7*5*2*(i*i)
\n" ); document.write( "Since \"i%2Ai=i%5E2=-1\" we get:
\n" ); document.write( "7*5*2*(-1)
\n" ); document.write( "Multiplying these numbers we get:
\n" ); document.write( "-70 \n" ); document.write( "
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