document.write( "Question 614658: Please help me solve this equation (sqrt6-6)(sqrt3+4) \n" ); document.write( "

Algebra.Com's Answer #386694 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"%28sqrt%286%29-6%29%28sqrt%283%29%2B4%29\"$
\n" ); document.write( "First of all, this is not an equation. There is no equals sign. It is an expression. And expressions are simplified, not solved.

\n" ); document.write( "Just as with any pair of binomials (two-term expressions), you use FOIL to multiply:
\n" ); document.write( "F: $\"sqrt%286%29%2Asqrt%283%29\"$
\n" ); document.write( "Using the property of radicals, $\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"$ , this becomes:
\n" ); document.write( " $\"sqrt%286%2A3%29+=+sqrt%2818%29\"$
\n" ); document.write( "And since 18 has a perfect square factor, $\"sqrt%2818%29\"$ will simplify:
\n" ); document.write( " $\"sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2Asqrt%282%29+=+3sqrt%282%29\"$

\n" ); document.write( "O: $\"sqrt%286%29%2A4+=+4sqrt%286%29\"$
\n" ); document.write( "I: $\"-6%2Asqrt%283%29+=+-6sqrt%283%29\"$
\n" ); document.write( "L: $\"-6%2A4+=+-12\"$

\n" ); document.write( "Putting this all together we get:
\n" ); document.write( "

\n" ); document.write( "None of these terms are like terms so they cannot be added. This expression (or, if you prefer subtractions, $\"3sqrt%282%29+%2B+4sqrt%286%29+-6sqrt%283%29+-12\"$ ) is the simplified expression. \n" ); document.write( "

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