document.write( "Question 78946: I need to rationalize the denominator of 5 over (7- radical 14). I get 1+ (radical 14 over 7). Is this the same as (7 + radical 14) over 7? Since 7/7 is 1, it should be equivalent. \n" ); document.write( "

Algebra.Com's Answer #56667 by fetter6(6) $\"\"$ $\"About$

You can put this solution on YOUR website!
Problem: Rationalize $\"5%2F%287-sqrt%2814%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Multiple the top and bottom by the conjugate of $\"7-sqrt%2814%29\"$ which is $\"7%2Bsqrt%2814%29\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"5%2F%287-sqrt%2814%29%29+%2A+%287%2Bsqrt%2814%29%29%2F%287%2Bsqrt%2814%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "The numerator becomes $\"5%287%2Bsqrt%2814%29%29=35%2B5sqrt%2814%29\"$
\n" ); document.write( "The denominator becomes $\"%287-sqrt%2814%29%29%287%2Bsqrt%2814%29%29=49-14=35\"$ \r
\n" ); document.write( "\n" ); document.write( "So the problem reduces to:\r
\n" ); document.write( "\n" ); document.write( " $\"%2835%2B5sqrt%2814%29%29%2F35=1%2Bsqrt%2814%29%2F7\"$ . So you are correct!\r
\n" ); document.write( "\n" ); document.write( "QED \n" ); document.write( "

\n" );