document.write( "Question 812624: Simplify the square root of -27 multiplied by the square root of -50 \n" ); document.write( "

Algebra.Com's Answer #489409 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
First of all, please try to post your questions under appropriate categories. This problem has nothing to do with conic sections. I have changed the category to a more appropriate one.

\n" ); document.write( " $\"sqrt%28-27%29%2Asqrt%28-50%29\"$
\n" ); document.write( "With negative radicands in square roots we are working with complex numbers. (\"Radicand\" is the name for the expression that appears inside a radical.) It is important to recognize the presence of complex numbers because it will dictate the proper procedure.

\n" ); document.write( "When working with complex numbers it is important to rewrite the expression in terms of \"i\" (which is defined as $\"sqrt%28-1%29\"$ ) before doing anything else:
\n" ); document.write( " $\"sqrt%28-1%2A27%29%2Asqrt%28-1%2A50%29\"$
\n" ); document.write( " $\"sqrt%28-1%29%2Asqrt%2827%29%2Asqrt%28-1%29%2Asqrt%2850%29\"$
\n" ); document.write( " $\"i%2Asqrt%2827%29%2Ai%2Asqrt%2850%29\"$

\n" ); document.write( "Now we can simplify the remaining square roots and then multiply or we can do it the other way around. Since I don't feel like multiplying 27 and 50 I choose to simplify first:
\n" ); document.write( " $\"i%2Asqrt%289%2A3%29%2Ai%2Asqrt%2825%2A2%29\"$
\n" ); document.write( " $\"i%2Asqrt%289%29%2Asqrt%283%29%2Ai%2Asqrt%2825%29%2Asqrt%282%29\"$
\n" ); document.write( " $\"i%2A3%2Asqrt%283%29%2Ai%2A5%2Asqrt%282%29\"$
\n" ); document.write( "Now we multiply:
\n" ); document.write( " $\"15i%5E2%2Asqrt%283%2A2%29\"$
\n" ); document.write( " $\"15%28-1%29%2Asqrt%286%29\"$ Since $\"i%5E2+=+-1\"$
\n" ); document.write( " $\"-15%2Asqrt%286%29\"$
\n" ); document.write( "This is the simplified result. \n" ); document.write( "

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