SOLUTION: 1/cube root of 4 + cube root of 5

Question 719718: 1/cube root of 4 + cube root of 5
Answer by jsmallt9(3758) (Show Source): 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:

But I'm pretty sure you intended:

Assuming that the expression is:

and the instructions are "Rationalize the denominator" (or something to that effect), then we will take advantage of the factoring pattern:

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 and the "b" is . If we multiply the numerator and denominator by the corresponding we will reach our goal:

In the denominator the pattern tells us how it works out:

which simplifies to:

then

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