document.write( "Question 1208223: simplify sqrt(-42) by sqrt(-6)
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Algebra.Com's Answer #846508 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Does \"sqrt(-42) by sqrt(-6)\" mean \r\n" );
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document.write( "\"sqrt(-42) MULTIPLIED by sqrt(-6)\", or\r\n" );
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document.write( "sqrt(-42) DIVIDED by sqrt(-6).\r\n" );
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document.write( "Be sure you specify which if you post again, for there is a big difference.\r\n" );
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document.write( "Either way, this gets into complex numbers when we have square roots (or any\r\n" );
document.write( "even roots of negative numbers.\r\n" );
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document.write( "We can't just multiply under the radicals like we can when there are only\r\n" );
document.write( "positive or zeros under root radicals.\r\n" );
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document.write( "If you meant this:\r\n" );
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document.write( "we can't multiply under those radicals.\r\n" );
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document.write( "We have to take out  first:\r\n" );
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document.write( "Now we have only positive numbers under the square radical. So now we\r\n" );
document.write( "can multiply under the radicals.  Also \r\n" );
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document.write( "If you meant:\r\n" );
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document.write( "sqrt(-42) DIVIDED by sqrt(-6).\r\n" );
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document.write( "To be on the safe side, we should not divide under the radicals if there are\r\n" );
document.write( "negative numbers under them.\r\n" );
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document.write( "Now we have only positive numbers under the radical, so we can divide them\r\n" );
document.write( "and get:\r\n" );
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document.write( "You may notice that if we had divided the negative numbers under the\r\n" );
document.write( "radicals, we would have gotten the right answer, but you can't trust it\r\n" );
document.write( "because sometimes it works and sometimes it doesn't.  [It might be \r\n" );
document.write( "interesting to find out when it works and when it doesn't.]\r\n" );
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document.write( "Maybe it always works for dividing but not for multiplying. I dunno. You\r\n" );
document.write( "find out!  \r\n" );
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document.write( "Edwin

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