document.write( "Question 1117168: solve Sqrt {2+sqrt {3}} \n" ); document.write( "
Algebra.Com's Answer #853350 by MathTherapy(10704)\"\" \"About 
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document.write( "solve Sqrt {2+sqrt {3}}\r\n" );
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document.write( "solve SIMPLIFY \"sqrt%282+%2B+sqrt%283%29%29\"\r\n" );
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document.write( "\"sqrt%282+%2B+sqrt%283%29%29\" = \"sqrt%281%282+%2B+sqrt%283%29%29%29\" = \"sqrt%28%282%282+%2B+sqrt%283%29%29%29%2F2%29\" ----- Multiplying RADICAND, \"2+%2B+sqrt%283%29\" by 1 = \"2%2F2\"\r\n" );
document.write( "                        = \"sqrt%28%284+%2B+2sqrt%283%29%29%2F2%29\"\r\n" );
document.write( "                        = \"sqrt%28%283+%2B+1+%2B+2sqrt%283%2A1%29%29%2F2%29\" ----- Replacing 4 with 3 + 1, and 3 with 3*1\r\n" );
document.write( "                        = \"sqrt%28%283+%2B+1+%2B+2sqrt%283%29%2Asqrt%281%29%29%2F2%29\"\r\n" );
document.write( "                        =  ---- Converting 3 to \"%28sqrt%283%29%29%5E2\", and 1 to \"%28sqrt%281%29%29%5E2\"\r\n" );
document.write( "The numerator, \"%28sqrt%283%29%29%5E2+%2B+%28sqrt%281%29%29%5E2+%2B+2sqrt%283%29%2Asqrt%281%29\" is in the form: \"%28a+%2B+b%29%5E2\", with a being \"sqrt%283%29\", and b being \"sqrt%281%29\"\r\n" );
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document.write( "                      So,  now becomes:\r\n" );
document.write( "                          \"sqrt%28%28%28sqrt%283%29+%2B+sqrt%281%29%29%5E2%29%2F2%29\" \r\n" );
document.write( "                          \"sqrt%28%28sqrt%283%29+%2B+sqrt%281%29%29%5E2%29%2Fsqrt%282%29%29\" --- Applying \"sqrt%28a%2Fb%29+=+sqrt%28a%29%2Fsqrt%28b%29\"\r\n" );
document.write( "                          \"%28sqrt%283%29+%2B+sqrt%281%29%29%2Fsqrt%282%29\" ----- Cancelling square and sqrt in NUMERATOR\r\n" );
document.write( "                          \"%28%28sqrt%283%29+%2B+sqrt%281%29%29%2Fsqrt%282%29%29+%2A+%28sqrt%282%29%2Fsqrt%282%29%29\" ------ Rationalizing DENOMINATOR\r\n" );
document.write( "                          \"sqrt%282%29%28sqrt%283%29+%2B+sqrt%281%29%29%2F%28sqrt%282%29%2Asqrt%282%29%29%29\" = \"highlight_green%28highlight%28%28sqrt%286%29+%2B+sqrt%282%29%29%2F2%29%29\"
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