# Thread: Rationalising a fourth root in the denominator

1. ## Rationalising a fourth root in the denominator

Help! I've been stuck on this for a few days now. I can rationalize square roots in the denominator as well as terms with square roots, but I'm not sure where to begin with a fourth root. Should I multiply top and bottom by $\displaystyle {\sqrt[4]{10}}$ or by $\displaystyle {\sqrt[4]{1000}}$ or by something else?

This is my problem:

$\displaystyle \frac{5-\sqrt10}{\sqrt[4]{10}}$

Help! I've been stuck on this for a few days now. I can rationalize square roots in the denominator as well as terms with square roots, but I'm not sure where to begin with a fourth root. Should I multiply top and bottom by $\displaystyle {\sqrt[4]{10}}$ or by $\displaystyle {\sqrt[4]{1000}}$ or by something else?

This is my problem:

$\displaystyle \frac{5-\sqrt10}{\sqrt[4]{10}}$
I believe I'd multiply by $\displaystyle \sqrt[4]{1000}$ to get that denominator to 10. Multiplying by $\displaystyle \sqrt[4]{10}$ won't get the job done.

3. $\displaystyle \begin{gathered} \sqrt[4]{{10^3 }} = \left( {10} \right)^{\frac{3} {4}} \hfill \\ \left[ {\left( {10} \right)^{\frac{1} {4}} } \right]\left[ {\left( {10} \right)^{\frac{3} {4}} } \right] = 10 \hfill \\ \end{gathered}$

4. Okay, I've worked through it and I come up with:

$\displaystyle \frac{\sqrt[4]{1000}-2\sqrt[4]{10}}{2}$

It gives me the same answer as the original equation when I plug it into my calculator, but is it in its simplest form?

5. Originally Posted by Plato
$\displaystyle \begin{gathered} \sqrt[4]{{10^3 }} = \left( {10} \right)^{\frac{3} {4}} \hfill \\ \left[ {\left( {10} \right)^{\frac{1} {4}} } \right]\left[ {\left( {10} \right)^{\frac{3} {4}} } \right] = 10 \hfill \\ \end{gathered}$
I'd do this; multiply top and bottom by 10^(3/4).
Also, how to do you big fractions like on your first post with the math function?