Question

Explain what is meant by the word rationalize in the phrase, “rationalize a denominator.”

Short answer

The phrase " rationalize the denominator" means the making the denominator of a fraction free from radicals. Thus, the word rationalize means to make the expression radical free.

Step-by-step solution

Step 1 Definition for the "rationalize the denominator".

The phrase " rationalize the denominator" means the making the denominator of a fraction free from radicals. Thus, the word rationalize means to make the expression radical free.

Step 2 Let us explain the phrase with an example.

Rationalize the denominator of $\frac{4}{\sqrt{5}}$as shown below.

First multiply numerator and denominator by $\sqrt{5}$.

$$\begin{gathered} \frac{4}{\sqrt{5}}=\frac{4.\sqrt{5}}{\sqrt{5}.\sqrt{5}} \\ =\frac{4\sqrt{5}}{5} \end{gathered}$$

Therefore, what is meant by the word 'rationalize' is explained.