document.write( "Question 65449This question is from textbook An Incremental Development
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\n" ); document.write( "\n" ); document.write( "6 times the square root of 7/5 - 2 times the square root of 5/7 - 3 times the square root of 140 \n" ); document.write( "

Algebra.Com's Answer #46040 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

Simplify: \r\n" );
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document.write( "6Ö7/5 - 2Ö5/7 - 3Ö140\r\n" );
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document.write( "We have to simplify each of the three radicals:\r\n" );
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document.write( "First term has this radical\r\n" );
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document.write( "     / 7\r\n" );
document.write( " \  / ---\r\n" );
document.write( "  \/   5\r\n" );
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document.write( "We must rationalize the denominator by multiplying\r\n" );
document.write( "under the radical by this fraction which equals 1:\r\n" );
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document.write( " 5\r\n" );
document.write( "---\r\n" );
document.write( " 5\r\n" );
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document.write( "      ________\r\n" );
document.write( "     / 7   5\r\n" );
document.write( " \  / ---×---    = \r\n" );
document.write( "  \/   5   5\r\n" );
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document.write( "      _____        __\r\n" );
document.write( "     / 35         Ö35      __\r\n" );
document.write( " \  / ----    =  ------ = Ö35/5 \r\n" );
document.write( "  \/   5²           5\r\n" );
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document.write( "So now we have\r\n" );
document.write( "  __       ___     ___\r\n" );
document.write( "6Ö35/5 - 2Ö5/7 - 3Ö140\r\n" );
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document.write( "The second term has this radical\r\n" );
document.write( "      _____\r\n" );
document.write( "     / 5\r\n" );
document.write( " \  / ---\r\n" );
document.write( "  \/   7\r\n" );
document.write( "\r\n" );
document.write( "We must rationalize the denominator by multiplying\r\n" );
document.write( "under the radical by this fraction which equals 1:\r\n" );
document.write( "\r\n" );
document.write( " 7\r\n" );
document.write( "---\r\n" );
document.write( " 7\r\n" );
document.write( "\r\n" );
document.write( "      ________\r\n" );
document.write( "     / 5   7\r\n" );
document.write( " \  / ---×---    = \r\n" );
document.write( "  \/   7   7\r\n" );
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document.write( "      _____        __\r\n" );
document.write( "     / 35         Ö35      __\r\n" );
document.write( " \  / ----    =  ------ = Ö35/7 \r\n" );
document.write( "  \/   7²           7\r\n" );
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document.write( "So now we have\r\n" );
document.write( "  __       __       ___\r\n" );
document.write( "6Ö35/5 - 2Ö35/7 - 3Ö140\r\n" );
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document.write( "The third term contains Ö140, which\r\n" );
document.write( "we simplify by writing 140 as 4×35\r\n" );
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document.write( "Ö140 = Ö4×35 = Ö4×Ö35 = 2×Ö35 = 2Ö35\r\n" );
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document.write( "So now we have \r\n" );
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document.write( "  __       __         __\r\n" );
document.write( "6Ö35/5 - 2Ö35/7 - 3·2Ö35\r\n" );
document.write( "              \r\n" );
document.write( "or\r\n" );
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document.write( "  __       __       __\r\n" );
document.write( "6Ö35/5 - 2Ö35/7 - 6Ö35\r\n" );
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document.write( "Now we factor out the common factor of Ö35\r\n" );
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document.write( "Ö35(6/5 - 2/7 - 6)\r\n" );
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document.write( "Then we get a common denominator, LCD = 35,\r\n" );
document.write( "inside the parentheses, and write\r\n" );
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document.write( "6/5 as 42/35\r\n" );
document.write( "2/7 as 10/35\r\n" );
document.write( "6 as 210/35\r\n" );
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document.write( "Ö35(42/35 - 10/35 - 210/35) =\r\n" );
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document.write( "Ö35(-178/35) =\r\n" );
document.write( "     __\r\n" );
document.write( "-178Ö35/35 \r\n" );
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document.write( "Edwin

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