document.write( "Question 1208689: Fill in the blanks with positive integers:
\n" ); document.write( "(3 + sqrt(6))^3 = ___ + ___ * sqrt(6) \n" ); document.write( "

Algebra.Com's Answer #847091 by math_tutor2020(3817) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Answer: 81 + 33*sqrt(6)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Work Shown
\n" ); document.write( " $\"%28a%2Bb%29%5E3+=+a%5E3+%2B+3a%5E2b%2B3ab%5E2+%2B+b%5E3\"$ Using the binomial theorem\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Plug in a = 3 and b = sqrt(6)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+27+%2B+27%2Asqrt%286%29+%2B+54+%2B+6%2Asqrt%286%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+%2827%2B54%29+%2B+%2827%2Asqrt%286%29%2B6%2Asqrt%286%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+81+%2B+%2827%2B6%29%2Asqrt%286%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+red%2881%29+%2B+red%2833%29%2Asqrt%286%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Here is another route which is a bit slower, but could be useful to know.
\n" ); document.write( " $\"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\"$ The FOIL rule can be used to confirm this or use the binomial theorem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E2+=+3%5E2+%2B+2%2A3%2Asqrt%286%29+%2B+%28sqrt%286%29%29%5E2\"$ Plug in a = 3 and b = sqrt(6)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E2+=+9+%2B+6%2Asqrt%286%29+%2B+6\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E2+=+15+%2B+6%2Asqrt%286%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Then,
\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+%283%2Bsqrt%286%29%29%283%2Bsqrt%286%29%29%5E2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+%283%2Bsqrt%286%29%29%2815+%2B+6%2Asqrt%286%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+x%2815+%2B+6%2Asqrt%286%29%29\"$ Let x = 3+sqrt(6)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+x%2A15+%2B+x%2A6%2Asqrt%286%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

Plug in x = 3+sqrt(6)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+45+%2B+15%2Asqrt%286%29%2B18%2Asqrt%286%29+%2B+36\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%283%2Bsqrt%286%29%29%5E3+=+red%2881%29+%2B+red%2833%29%2Asqrt%286%29\"$
\n" ); document.write( "Therefore, 81 and 33 go in those blanks in the order mentioned.
\n" ); document.write( " \n" ); document.write( "

\n" );