document.write( "Question 1140877: Without a calculator find, 1/[sqrt(1) + sqrt(2)] + 1/[sqrt(2) + sqrt(3)] + 1/[sqrt(3) + sqrt(4)] + ...+ 1/[sqrt(15) + sqrt(16)] \n" ); document.write( "

Algebra.Com's Answer #761382 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Every aggregate   is equal to  .\r\n" );
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document.write( "    // after multiplication the denominator and the numerator by  \r\n" );
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document.write( "After summing all such aggregates from m = 1 to m = 15 you get the final answer\r\n" );
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document.write( "    ,   which is equal to  4 - 1 = 3.\r\n" );
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document.write( "(all other intermediate terms cancel each other on the way).\r\n" );
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document.write( "ANSWER.  3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Amazing calculations with fractions that contain quadratic irrationalities in denominators, Problem 4\r
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