document.write( "Question 389875: please simplify this expression:
\n" ); document.write( "5 square root 15 times (-2 square root 3) \n" ); document.write( "

Algebra.Com's Answer #276941 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"5sqrt%2815%29%2A%28-2sqrt%283%29%29\"$
\n" ); document.write( "This expression is all multiplication. So we can use the Commutative and Associative properties to rearrange the order and grouping to:
\n" ); document.write( " $\"%285%2A%28-2%29%29%28sqrt%2815%29%2Asqrt%283%29%29\"$
\n" ); document.write( "Multiplying the first part is simple. We use the property of radicals, $\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"$ , to multiply the square roots:
\n" ); document.write( " $\"-10sqrt%2845%29\"$
\n" ); document.write( "Last of all we simplify. We can simplify $\"sqrt%2845%29\"$ because it has a perfect square factor, 9:
\n" ); document.write( " $\"-10sqrt%289%2A5%29\"$
\n" ); document.write( "Now we can use the property of radicals (from right to left) to separate the factors into their won square roots:
\n" ); document.write( " $\"-10sqrt%289%29%2Asqrt%285%29\"$
\n" ); document.write( "Since $\"sqrt%289%29+=+3\"$ this becomes:
\n" ); document.write( " $\"-10%2A3%2Asqrt%285%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"-30sqrt%285%29\"$ \n" ); document.write( "

\n" );