document.write( "Question 368718: How do I simplify -4 times the square root of 24 \n" ); document.write( "

Algebra.Com's Answer #262878 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"-4sqrt%2824%29\"$
\n" ); document.write( "Simplifying square roots is done by finding perfect square factors (other than 1) of the radicand (the expression inside a radical). If there are no perfect square factors of the radicand, the square root cannot be simplified.\n" ); document.write( "So we will be looking for perfect square factors of your radicand, 24. Among the factors of 24, only one is a perfect suqare: 4. So we rewrite the square root in a factored form, using the perfect square factor:
\n" ); document.write( " $\"-4sqrt%284%2A6%29\"$
\n" ); document.write( "Next 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 factors into their own square roots:
\n" ); document.write( " $\"-4sqrt%284%29%2Asqrt%286%29\"$
\n" ); document.write( "Now that the perfect square factor is in its own square root, we can replace it. Since $\"sqrt%284%29+=+2\"$ we will replace it with 2:
\n" ); document.write( " $\"-4%2A2%2Asqrt%286%29\"$
\n" ); document.write( "Last of all we multiply the -4 and the 2:
\n" ); document.write( " $\"-8%2Asqrt%286%29\"$ \n" ); document.write( "

\n" );