document.write( "Question 186806This question is from textbook saxon algebra 2
\n" ); document.write( ": Simplify. \"sqrt%28128%29+-+sqrt%2875%29+-+sqrt%2898%29\"
\n" ); document.write( "The square root 75 is confusing. What do you do with that? \n" ); document.write( "
Algebra.Com's Answer #140026 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Solution by Edwin:
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document.write( "\"sqrt%28128%29+-+sqrt%2875%29+-+sqrt%2898%29\"\r\n" );
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document.write( "Since this involves square roots, we make a list of squares\r\n" );
document.write( "greater than \"1%5E2\".\r\n" );
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document.write( "\"2%5E2+=+4\"\r\n" );
document.write( "\"3%5E2=9\"\r\n" );
document.write( "\"4%5E2=16\"\r\n" );
document.write( "\"5%5E2=25\"\r\n" );
document.write( "\"6%5E2=36\"\r\n" );
document.write( "\"7%5E2=49\"\r\n" );
document.write( "\"8%5E2=64\"\r\n" );
document.write( "\"9%5E2=81\"\r\n" );
document.write( "\"10%5E2=100\"\r\n" );
document.write( "\"11%5E2=121\"\r\n" );
document.write( "\"12%5E2=144\"\r\n" );
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document.write( "You have 128, 75, and 98\r\n" );
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document.write( "For 128, find the largest square on the right \r\n" );
document.write( "in the list above that will divide evenly into\r\n" );
document.write( "128.  This is 64.  So we write 128 as 64*2.\r\n" );
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document.write( "For 75, find the largest square on the right \r\n" );
document.write( "in the list above that will divide evenly into\r\n" );
document.write( "75.  This is 25.  So we write 75 as 25*3.\r\n" );
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document.write( "For 98, find the largest square on the right \r\n" );
document.write( "in the list above that will divide evenly into\r\n" );
document.write( "98.  This is 49.  So we write 98 as 49*2.\r\n" );
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document.write( "So instead of\r\n" );
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document.write( "\"sqrt%28128%29+-+sqrt%2875%29+-+sqrt%2898%29\"\r\n" );
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document.write( "we write\r\n" );
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document.write( "\"sqrt%2864%2A2%29+-+sqrt%2825%2A3%29+-+sqrt%2849%2A2%29\"\r\n" );
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document.write( "Now we write the square roots of the products as\r\n" );
document.write( "the product of the square roots:\r\n" );
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document.write( "\"sqrt%2864%29sqrt%282%29+-+sqrt%2825%29sqrt%283%29+-+sqrt%2849%29sqrt%282%29\"\r\n" );
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document.write( "We know the square roots of 64,25, and 49 are 8,5, and 7,\r\n" );
document.write( "so now we have\r\n" );
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document.write( "\"8sqrt%282%29+-+5sqrt%283%29+-+7sqrt%282%29\"\r\n" );
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document.write( "Now the first and third terms are like terms,\r\n" );
document.write( "so \r\n" );
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document.write( "8 square roots of 2 minus 7 square roots of two equals\r\n" );
document.write( "1 square root of 2.  So combining the first and third\r\n" );
document.write( "terms we have \r\n" );
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document.write( "\"1sqrt%282%29+-+5sqrt%283%29\"\r\n" );
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document.write( "but we don't need the 1\r\n" );
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document.write( "\"sqrt%282%29+-+5sqrt%283%29\"\r\n" );
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document.write( "You cannot go further than this, so you stop here!\r\n" );
document.write( "This is the simplest radical form.\r\n" );
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document.write( "Edwin
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