document.write( "Question 719718: 1/cube root of 4 + cube root of 5 \n" ); document.write( "
Algebra.Com's Answer #441513 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
First of all, please
  • Include the instructions for the problem. Don't assume that there is only one obvious thing to do with an expression.
  • Put multiple-term numerators and denominators in parentheses. What you posted meant:
    \n" ); document.write( "\"1%2Froot%283%2C+4%29+%2B+root%283%2C+5%29\"
    \n" ); document.write( "But I'm pretty sure you intended:
    \n" ); document.write( "\"1%2F%28root%283%2C+4%29+%2B+root%283%2C+5%29%29\"
Assuming that the expression is:
\n" ); document.write( "\"1%2F%28root%283%2C+4%29+%2B+root%283%2C+5%29%29\"
\n" ); document.write( "and the instructions are \"Rationalize the denominator\" (or something to that effect), then we will take advantage of the factoring pattern:
\n" ); document.write( "\"%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29+=+a%5E3%2Bb%5E3\"
\n" ); document.write( "This pattern shows how a two-term expression times a certain three-term expression results in an expression of perfect cubes. The denominator we have to rationalize is a two-term expression which matches the pattern of (a+b). So the pattern shows how to turn that into an expression of perfect cubes. Since the cube of a cube root is rational, this is our path to a solution. In our denominator, the \"a\" is \"root%283%2C4%29\" and the \"b\" is \"root%283%2C5%29\". If we multiply the numerator and denominator by the corresponding \"a%5E2-ab%2Bb%5E2\" we will reach our goal:
\n" ); document.write( "
\n" ); document.write( "In the denominator the pattern tells us how it works out:
\n" ); document.write( "
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"%28root%283%2C16%29-root%283%2C20%29%2Broot%283%2C+25%29%29%2F%284%2B5%29\"
\n" ); document.write( "then
\n" ); document.write( "\"%28root%283%2C16%29-root%283%2C20%29%2Broot%283%2C+25%29%29%2F9\" \n" ); document.write( "
\n" );