document.write( "Question 289695: -4√112-3√128+3√63-2√7 simplify \n" ); document.write( "
Algebra.Com's Answer #209966 by jsmallt9(3759)\"\" \"About 
You can put this solution on YOUR website!
\"-4sqrt%28112%29-3sqrt%28128%29%2B3sqrt%2863%29-2sqrt%287%29\"
\n" ); document.write( "The primary part of simplifying expressions with square roots is to factor out perfect squares in each square root, if any:
\n" ); document.write( "\"-4sqrt%2816%2A7%29-3sqrt%2864%2A2%29%2B3sqrt%289%2A7%29-2sqrt%287%29\"
\n" ); document.write( "Then you use the property of radicals, \"root%28a%2C+x%2Ay%29+=+root%28a%2C+x%29%2Aroot%28a%2C+y%29\", to separate the perfect square factors into their own square roots:
\n" ); document.write( "
\n" ); document.write( "Now we can replace the square roots of the perfect squares:
\n" ); document.write( "\"-4%2A4%2Asqrt%287%29-3%2A8%2Asqrt%282%29%2B3%2A3%2Asqrt%287%29-2sqrt%287%29\"
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"-16sqrt%287%29-24sqrt%282%29%2B9sqrt%287%29-2sqrt%287%29\"
\n" ); document.write( "The first, third and fourth terms are like terms which we can add and subtract. This gives us:
\n" ); document.write( "\"-9sqrt%287%29-24sqrt%282%29\"
\n" ); document.write( "This is the simplified expression.
\n" ); document.write( " \n" ); document.write( "
\n" );