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\( \begin{array}{l}\text { Rationalize } \\ \text { the } \\ \text { denominator. }\end{array} \quad \sqrt{\frac{14}{3}}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.) \( \sqrt{\frac{14}{3}} \)

Ask by Bryant Mann. in the United States
Jan 22,2025

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\( \sqrt{\frac{14}{3}} = \frac{\sqrt{42}}{3} \)

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The Deep Dive

To rationalize the denominator of \( \sqrt{\frac{14}{3}} \), you can multiply both the numerator and the denominator by \( \sqrt{3} \). This gives you: \[ \sqrt{\frac{14}{3}} = \frac{\sqrt{14} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{42}}{3} \] So, the rationalized form is \( \frac{\sqrt{42}}{3} \). To ensure you have the simplest form, remember that the square root cannot be simplified further because 42 does not have any perfect square factors. Thus, \( \frac{\sqrt{42}}{3} \) is your final answer!

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