document.write( "Question 38829: 
Write in simplified radical form by rationalizing the denominator.\r\n" );
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document.write( "  Ö3 - 2\r\n" );
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document.write( " -5Ö3 + 8
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Algebra.Com's Answer #24320 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
To rationalize the denominator means to get rid of any\r\n" );
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document.write( "   _\r\n" );
document.write( "  Ö3 - 2\r\n" );
document.write( "——————————\r\n" );
document.write( " -5Ö3 + 8\r\n" );
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document.write( "Since the denominator contains more than one term, at \r\n" );
document.write( "least one of which is a square root radical.\r\n" );
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document.write( "We create the \"conjugate surd\" of the denominator by \r\n" );
document.write( "changing only the sign of one of the (in this 'the only')\r\n" );
document.write( "square root radical term. This expression we create is \r\n" );
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document.write( "+5Ö3 + 8\r\n" );
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document.write( "Then we place it over itself:\r\n" );
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document.write( "    _\r\n" );
document.write( "  5Ö3 + 8\r\n" );
document.write( " ————————\r\n" );
document.write( "  5Ö3 + 8\r\n" );
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document.write( "which equals 1.  Therefore we can multiple the original\r\n" );
document.write( "expression by this fraction which does not change its \r\n" );
document.write( "numerical value, because we can multiply any expression\r\n" );
document.write( "by 1 without changing its numerical value.\r\n" );
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document.write( "   _           _\r\n" );
document.write( "  Ö3 - 2     5Ö3 + 8\r\n" );
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document.write( " -5Ö3 + 8    5Ö3 + 8\r\n" );
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document.write( "Indicate the product of the numerators and denominators \r\n" );
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document.write( "  Ö3 - 2     5Ö3 + 8\r\n" );
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document.write( " -5Ö3 + 8    5Ö3 + 8\r\n" );
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document.write( "   _        _\r\n" );
document.write( " (Ö3 - 2)(5Ö3 + 8)\r\n" );
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document.write( "(-5Ö3 + 8)(5Ö3 + 8)\r\n" );
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document.write( "Use FOIL to multiply out the numerator and denominator:\r\n" );
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document.write( "    _    _      _      _\r\n" );
document.write( "  (Ö3)(5Ö3) + 8Ö3 - 10Ö3 - 16\r\n" );
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document.write( "(-5Ö3)(5Ö3)  - 40Ö3 + 40Ö3 + 64\r\n" );
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document.write( "   5·3 - 2Ö3 - 16\r\n" );
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document.write( "    -25·3 + 64\r\n" );
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document.write( "   15 - 2Ö3 - 16\r\n" );
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document.write( "    -75 + 64\r\n" );
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document.write( "  -1 - 2Ö3 \r\n" );
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document.write( "    -11\r\n" );
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document.write( "to get rid of the negative signs multiply by the\r\n" );
document.write( "fraction (-1)/(-1)\r\n" );
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document.write( " -1    (-1 - 2Ö3)   \r\n" );
document.write( "———— × —————————— \r\n" );
document.write( " -1        -11 \r\n" );
document.write( "           _\r\n" );
document.write( " -1(-1 - 2Ö3)   \r\n" );
document.write( "—————————————— \r\n" );
document.write( "   (-1)(-11)\r\n" );
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document.write( "        _\r\n" );
document.write( "  1 + 2Ö3\r\n" );
document.write( " ————————— \r\n" );
document.write( "    11\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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