document.write( "Question 77785: We are studying nth roots and rational exponents and I need help!
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\n" ); document.write( "4/square root of 176 + 4/square root of 11=
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Algebra.Com's Answer #55781 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We are studying nth roots and rational exponents \r\n" );
document.write( "and I need help! \r\n" );
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document.write( "Problem:\r\n" );
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document.write( "4/square root of 176 + 4/square root of 11=\r\n" );
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document.write( "\"4%2Fsqrt%28176%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "We begin by breaking 176 down into prime factors:\r\n" );
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document.write( "176 = 2x88 = 2x2x44 = 2x2x4x11 = 2x2x2x2x11\r\n" );
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document.write( "11 is already a prime number\r\n" );
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document.write( "So we have\r\n" );
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document.write( "\"4%2Fsqrt%282%2A2%2A2%2A2%2A11%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "Group the like factors into pairs:\r\n" );
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document.write( "\"4%2Fsqrt%28%282%2A2%29%2A%282%2A2%29%2A11%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "Write each pair as a square (of 2):\r\n" );
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document.write( "\"4%2Fsqrt%28%282%5E2%29%2A%282%5E2%29%2A%2811%29%29+%2B+4%2Fsqrt%2811%29\" \r\n" );
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document.write( "Distribute the Ö over its factors:\r\n" );
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document.write( "\"4%2F%28sqrt%282%5E2%29%2Asqrt%282%5E2%29%2Asqrt%2811%29%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "Now the square root of the square of a number is\r\n" );
document.write( "just the number, so the square root of 2 squared is\r\n" );
document.write( "just 2.\r\n" );
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document.write( "\"4%2F%282%2A2%2Asqrt%2811%29%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "Now the \"2%2A2\" on the bottom is just \"4\"\r\n" );
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document.write( "\"4%2F%284%2Asqrt%2811%29%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "Now we can cancel the \"4\"'s:\r\n" );
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document.write( "\"1%2Fsqrt%2811%29+%2B+4%2Fsqrt%2811%29\"\r\n" );
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document.write( "Since the two fractions have a common\r\n" );
document.write( "denominator, then we can just add the\r\n" );
document.write( "two numerators and place it over the common\r\n" );
document.write( "denominator:\r\n" );
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document.write( "\"5%2Fsqrt%2811%29\"\r\n" );
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document.write( "If your teacher wants you to rationalize\r\n" );
document.write( "the denominator and get the answer\r\n" );
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document.write( "\"%285sqrt%2811%29%29%2F11\"\r\n" );
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document.write( "then post again asking how to rationalize\r\n" );
document.write( "the denominator.\r\n" );
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document.write( "Problem: How do you type in the square root of problems \r\n" );
document.write( "using symbols?\r\n" );
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document.write( "Take the example \"sqrt%28176%29\"\r\n" );
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document.write( "I'll have to tell you in steps, because if I type it on \r\n" );
document.write( "here like you are to type it in you will just show up as\r\n" );
document.write( "\"sqrt%28176%29\"\r\n" );
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document.write( "1. Type three braces in a row { { { but don't skip a space\r\n" );
document.write( "   between them as I did here. I skipped spaces between\r\n" );
document.write( "   them here to keep the program from thinking I am\r\n" );
document.write( "   starting a problem and giving an error message.\r\n" );
document.write( "   These are open braces, not open parentheses. \r\n" );
document.write( "   The shifted key immediately to the right of the P key \r\n" );
document.write( "   on your keyboard gives open braces.\r\n" );
document.write( "2. On the same line immediately after that type sqrt(176)\r\n" );
document.write( "   That's parentheses, (shifted 9 and 0), not braces.\r\n" );
document.write( "3. On the same line immediately after that type }}}\r\n" );
document.write( "   Those are close braces, the shifted key just after the\r\n" );
document.write( "   key which when shifted gives the open braces.\r\n" );
document.write( "4. When you post your problem it will appear this way:\"sqrt%28176%29\"\r\n" );
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document.write( "Edwin
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