# To rationalize: Each numerator. Assume that variables represent positive real numbers. Given: An expression : displaystylefrac{{sqrt[{{3}}]{{9}}}}{{7}}.

To rationalize:
Each numerator. Assume that variables represent positive real numbers.
Given: An expression : $$\displaystyle\frac{{\sqrt[{{3}}]{{9}}}}{{7}}.$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Caren

Concept used:
In order to rationalize the numerator of an expression, we multiply in the numerator and denominator with such a term/expression such that we don't have any radicals left in the numerator upon simplifying.
Calcucation:
Let us rationalize the numerator as shown below:
$$\displaystyle\frac{{\sqrt[{{3}}]{{9}}}}{{7}}$$ (Given expression)
$$\displaystyle\Rightarrow\frac{{\sqrt[{{3}}]{{9}}}}{{7}}\cdot\frac{{\sqrt[{{3}}]{{3}}}}{{\sqrt[{{3}}]{{3}}}}\ \text{(multiplying fraction by}\ \displaystyle{\sqrt[{{3}}]{{3}}})$$
$$\displaystyle\Rightarrow\frac{{{\sqrt[{{3}}]{{9}}}\cdot{\sqrt[{{3}}]{{3}}}}}{{{7}\cdot{\sqrt[{{3}}]{{3}}}}}$$
$$\displaystyle\Rightarrow\frac{{\sqrt[{{3}}]{{{9}\cdot{3}}}}}{{{7}{\sqrt[{{3}}]{{3}}}}}{\left({A}{p}{p}{l}{y}\ integer{\sqrt[{{n}}]{{a}}}\cdot{\sqrt[{{n}}]{{b}}}={\sqrt[{{n}}]{{{a}{b}}}}\right)}$$
$$\displaystyle\Rightarrow\frac{{\sqrt[{{3}}]{{27}}}}{{{7}{\sqrt[{{3}}]{{3}}}}}$$
$$\displaystyle\Rightarrow\frac{{\sqrt[{{3}}]{{{3}^{3}}}}}{{{7}{\sqrt[{{3}}]{{3}}}}}$$
$$\displaystyle\Rightarrow\frac{3}{{{7}{\sqrt[{{3}}]{{3}}}}}{\left({A}{p}{p}{l}{y}\ integer{\sqrt[{{n}}]{{{a}^{n}}}}={a}\right)}$$
Therefore, the rationalized form of the given expression would be $$\displaystyle\frac{3}{{{7}{\sqrt[{{3}}]{{3}}}}}.$$