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

Question

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

UpStudy AI · Accepted Answer

To rationalize the denominator of the expression $$\sqrt{\frac{17}{3}}$$, follow these steps:

1. **Express the Square Root as a Fraction:**
   
   $$
   \sqrt{\frac{17}{3}} = \frac{\sqrt{17}}{\sqrt{3}}
   $$

2. **Rationalize the Denominator:**
   
   Multiply both the numerator and the denominator by $$\sqrt{3}$$ to eliminate the square root from the denominator:

$$
   \frac{\sqrt{17}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{17} \times \sqrt{3}}{3} = \frac{\sqrt{51}}{3}
   $$

3. **Simplify the Expression:**
   
   The expression $$\frac{\sqrt{51}}{3}$$ is the rationalized and simplified form of the original expression.

**Final Answer:**

$$
\sqrt{\frac{17}{3}} = \frac{\sqrt{51}}{3}
$$
$$ \sqrt{\frac{17}{3}} = \frac{\sqrt{51}}{3} $$

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