document.write( "Question 275568: multiply and simplify\r
\n" ); document.write( "\n" ); document.write( "sqroot 12a^2b multiply sqroot15ab^2 \n" ); document.write( "

Algebra.Com's Answer #200992 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"sqrt%28+12a%5E2b%29%2A+sqrt%2815ab%5E2%29\"$
\n" ); document.write( "One of the properties of radicals is: $\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"$
\n" ); document.write( "We will ue this property in both \"directions\". We will start by using it to multiply the two square roots into one:
\n" ); document.write( " $\"sqrt%28+12a%5E2b%2A15ab%5E2%29\"$
\n" ); document.write( "Simplifying the radicand (the expression inside a radical) we get:
\n" ); document.write( " $\"sqrt%28+180a%5E3b%5E3%29\"$
\n" ); document.write( "The last stage is to simplify the square root. This involves finding factors of the radicand that are perfect squares:
\n" ); document.write( " $\"sqrt%28+36%2A5%2Aa%5E2%2Aa%2Ab%5E2%2Ab%29\"$
\n" ); document.write( "Now we will use the property in the other direction to separate the factors into their own square roots:
\n" ); document.write( " $\"sqrt%28+36%29%2Asqrt%285%29%2Asqrt%28a%5E2%29%2Asqrt%28a%29%2Asqrt%28b%5E2%29%2Asqrt%28b%29\"$
\n" ); document.write( "Simplifying the square roots of the perfect squares we get:
\n" ); document.write( " $\"6%2Asqrt%285%29%2Aa%2Asqrt%28a%29%2Ab%2Asqrt%28b%29\"$
\n" ); document.write( "And finally we'll use the Commutative Property of Multiplication to rearrange the factors and our property of radcials to re-combine all the remaining square roots:
\n" ); document.write( " $\"6ab%2Asqrt%285ab%29\"$ \n" ); document.write( "

\n" );