Question

Rationalize the denominator. Assume variables represent non-negative values.

Answer 1

So, we have the cube root of y in the denominator. What would we need to multiply the denominator by to make this rational?

Answer 2

I really don't know.

Answer 3

We know:
\[(\sqrt[3]{y})^3 = \sqrt[3]{y}\sqrt[3]{y}\sqrt[3]{y} = y\]

Using this information, we see that we need to multiply the denominator by the cube root of y, twice.

Answer 4

Now, if we do the same thing to the numerator, we didn't change the fraction at all.

So multiply the top by the same factor.

Answer 5

Do I multiply it by 2^3?

Answer 6

Nope. I'll show you this one so you can see what I'm trying to say.

Answer 7

\[\frac{2}{\sqrt[3]{y}} = \frac{\sqrt[3]{y}\sqrt[3]{y}}{\sqrt[3]{y}\sqrt[3]{y}} \times \frac{2}{\sqrt[3]{y}} = \frac{2 (\sqrt[3]{y})^2}{y}\]

Answer 8

I got it now.