\begin{tabular}{l|l}\( \begin{array}{l}\text { Rationalize the } \\ \text { denominator. }\end{array} \) & \( \sqrt{\frac{17}{3}}=\square \) \\ \( \begin{array}{l}\frac{17}{3}\end{array} \) & \( \begin{array}{l}\text { (Simplify your answer. Type an exact answer, using radicals as needed.) }\end{array} \) \\ \end{tabular}

To rationalize the denominator for the expression \( \sqrt{\frac{17}{3}} \), you can rewrite it as \( \frac{\sqrt{17}}{\sqrt{3}} \). To eliminate the square root in the denominator, multiply the numerator and denominator by \( \sqrt{3} \). This gives you: \[ \frac{\sqrt{17} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{\sqrt{51}}{3} \] So, the rationalized form is \( \frac{\sqrt{51}}{3} \). In practical terms, rationalizing the denominator is not just about eliminating square roots; it often makes calculations easier, especially in fractions. For example, when adding or subtracting fractions, having a rational denominator clears up the arithmetic, making it simpler to manage the operations. It’s like tidying up your workspace before diving into a project—everything just flows better!