document.write( "Question 78945: I need to simplify the cube root of -60 over the cube root of 120. I think it is the negative of the cube root of 4 over 2, but I am not certain. \n" ); document.write( "
Algebra.Com's Answer #56663 by Edwin McCravy(20055)\"\" \"About 
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I need to simplify the cube root of -60 over the cube root of 120. I think it is the negative of the cube root of 4 over 2, but I am not certain.
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document.write( "I think you're right:\r\n" );
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document.write( "\"root%283%2C-60%29%2Froot%283%2C120%29\" =\r\n" );
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document.write( "\"root%283%2C+%28-60%29%2F120%29+\" =\r\n" );
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document.write( "\"root%283%2C-1%2F2%29\"\r\n" );
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document.write( "Rationalize the denominator.\r\n" );
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document.write( "The denominator needs 2 more factors\r\n" );
document.write( "of 2 to become a perfect cube, so\r\n" );
document.write( "we multiply the fraction under the\r\n" );
document.write( "radical by 2*2.  But if you\r\n" );
document.write( "multiply the denominator by 2*2\r\n" );
document.write( "you must multiply the numerator by\r\n" );
document.write( "2*2 also.\r\n" );
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document.write( "\"root%283%2C%28-1%2A2%2A2%29%2F%282%2A2%2A2%29%29\"\r\n" );
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document.write( "The 2*2*2 on the bottom can be\r\n" );
document.write( "written as 2³, and the 2*2 in the\r\n" );
document.write( "top can be written as 4\r\n" );
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document.write( "\"root%283%2C%28-1%2A4%29%2F2%5E3%29\"\r\n" );
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document.write( "Take cube roots of top and bottom\r\n" );
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document.write( "\"root%283%2C-1%2A4%29%2Froot%283%2C2%5E3%29\"\r\n" );
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document.write( "Take individual cube roots of -1 and 4\r\n" );
document.write( "in the top and taking the cube root of \r\n" );
document.write( "the bottom jsut gives 2\r\n" );
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document.write( "\"%28root%283%2C+-1%29root%283%2C4%29%29%2F2\"\r\n" );
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document.write( "The cube root of -1 is just -1\r\n" );
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document.write( "\"%28-1%2Aroot%283%2C4%29%29%2F2\" \r\n" );
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document.write( "or just\r\n" );
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document.write( "\"-root%283%2C4%29%2F2\"\r\n" );
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document.write( "Yes, you're right.\r\n" );
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document.write( "Edwin
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