document.write( "Question 350866: Multiply and simplify. Assume that all variables represent nonnegative numbers
\n" ); document.write( "(-5sqrt6)(2sqrt3) \n" ); document.write( "

Algebra.Com's Answer #250800 by jsmallt9(3758) $\"\"$ $\"About$

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$\"%28-5sqrt%286%29%29%282sqrt%283%29%29\"$
\n" ); document.write( "Since this expression is all multiplication and since multiplication is commutative and associative, we change change the grouping and/or order in any way we choose. So I am going to rearrage the factors so that the coefficients are together and grouped and the square roots are together and grouped:
\n" ); document.write( " $\"%28%28-5%29%282%29%29%28sqrt%286%29%2Asqrt%283%29%29\"$
\n" ); document.write( "The first part is easy to multiply. To multiply the square roots we need to know a basic property of radicals: $\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"$ . We can use this to multiply square roots. Now we have:
\n" ); document.write( " $\"%28-10%29%28sqrt%286%2A3%29%29\"$
\n" ); document.write( "which simplifies to
\n" ); document.write( " $\"-10sqrt%2818%29\"$
\n" ); document.write( "We are almost done. Just like you should reduce/simplify answers that are fractions, you also should simplify square roots. To simplify a square root you look for perfect square factors in the radicand (the expression inside the square root). Since 18 has a perfect square factor, 18 = 9*2, we can simplify, using the property we used eariler:
\n" ); document.write( " $\"-10sqrt%289%2A2%29\"$
\n" ); document.write( " $\"-10sqrt%289%29%2Asqrt%282%29\"$
\n" ); document.write( "Since $\"sqrt%289%29+=+3\"$ :
\n" ); document.write( " $\"-10%2A3%2Asqrt%282%29\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"-30sqrt%282%29\"$ \n" ); document.write( "

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