sibuzwaW

2020-12-12

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

Caren

Expert

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:
$\frac{\sqrt[3]{9}}{7}$ (Given expression)

$⇒\frac{\sqrt[3]{9}\cdot \sqrt[3]{3}}{7\cdot \sqrt[3]{3}}$

$⇒\frac{\sqrt[3]{27}}{7\sqrt[3]{3}}$
$⇒\frac{\sqrt[3]{{3}^{3}}}{7\sqrt[3]{3}}$

Therefore, the rationalized form of the given expression would be $\frac{3}{7\sqrt[3]{3}}.$

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