document.write( "Question 550173: 4√3+2√7-4√18 how can u simplfy it. I know you simplify each radical then combine but i do not know how to simplify a radical \n" ); document.write( "

Algebra.Com's Answer #358504 by Edwin McCravy(20086) $\"\"$ $\"About$

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4√3+2√7-4√18
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document.write( "You can't do much with that, except to simplify the\r\n" );
document.write( "last term.  Are you sure you didn't copy something\r\n" );
document.write( "wrong?\r\n" );
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document.write( " +  - \r\n" );
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document.write( "We can't break or 3 or 7, but we can break up 18\r\n" );
document.write( "into primes like this 2×3×3 and since there are two 3's \r\n" );
document.write( "there, that's 9, which is a perfect square. And we know\r\n" );
document.write( "that the square root of 9 is 3. So we copy everything\r\n" );
document.write( "over and write 9×2 instead of 18:\r\n" );
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document.write( " +  - \r\n" );
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document.write( "The square root of a product (multiplication) is the\r\n" );
document.write( "product (multiplication) of the square roots, so we\r\n" );
document.write( "can write  as  \r\n" );
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document.write( " +  - \r\n" );
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document.write( "and since we know that  is 3, we can write\r\n" );
document.write( "that last term up there as \r\n" );
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document.write( " +  - 4×3×\r\n" );
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document.write( "and since 4×3 is 12 we can have\r\n" );
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document.write( "4 + 2 - 12\r\n" );
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document.write( "But there is nothing else you can do in the way of\r\n" );
document.write( "simplifying radicals.  \r\n" );
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document.write( "If that 3 had been a 2, or the 7 had been a 2 or a 3\r\n" );
document.write( "or the 2 a 7, then we could have combined some terms, \r\n" );
document.write( "but as it is all we could do was simplify the last term\r\n" );
document.write( "and leave the first two terms as they were to begin with.\r\n" );
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document.write( "There is one thing we can do, but it it is not necessary,\r\n" );
document.write( "and that is to take out a 2 factor:\r\n" );
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document.write( "2( +  - )\r\n" );
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document.write( "Edwin

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