document.write( "Question 280777: what does the expression the square root of 90 x the square root of 40 - the sqaure root of 8 x the square root of 18 simplifies to what \n" ); document.write( "
Algebra.Com's Answer #204437 by jsmallt9(3758)\"\" \"About 
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\"sqrt%2890%29%2Asqrt%2840%29+-+sqrt%288%29%2Asqrt%2818%29\"
\n" ); document.write( "We could multiply the square roots first but we would get large radicands to simplify. Instead we'll simplify the square roots first. Simplifying square roots involves factoring out perfect square factors:
\n" ); document.write( "\"sqrt%289%2A10%29%2Asqrt%284%2A10%29+-+sqrt%284%2A2%29%2Asqrt%289%2A2%29\"
\n" ); document.write( "Using the property of radicals, \"root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29\", to separate the perfect square factors into their own square roots:
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\n" ); document.write( "Now we can replace the square roots of the perfect squares:
\n" ); document.write( "\"3%2Asqrt%2810%29%2A2%2Asqrt%2810%29+-+2%2Asqrt%282%29%2A3%2Asqrt%282%29\"
\n" ); document.write( "Within the two products we can use the Commutative and Associative properties to rearrange the order and grouping:
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\n" ); document.write( "Multiplying we get:
\n" ); document.write( "\"6%2A10+-+6%2A2\"
\n" ); document.write( "\"60+-+12\"
\n" ); document.write( "Subtracting we get:
\n" ); document.write( "48

\n" ); document.write( "If you had multiplied first you would get:
\n" ); document.write( "\"sqrt%283600%29+-+sqrt%28144%29\"
\n" ); document.write( "These cannot be subtracted because they are like terms. But you can simplify the two square roots. They end up being nice whole numbers we can be subtracted and this subtraction, if you've done everything correctly, results in 48. \n" ); document.write( "
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