$$ \sqrt{\frac{10}{11}}=\square $$ (Simplify your answer, including any radicals.

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UpStudy AI · Accepted Answer

To simplify the expression $$ \sqrt{\frac{10}{11}} $$, we can rationalize the denominator. Here's how you can do it step by step:

1. **Separate the Square Root:**
   
   $$
   \sqrt{\frac{10}{11}} = \frac{\sqrt{10}}{\sqrt{11}}
   $$

2. **Rationalize the Denominator:**
   
   To eliminate the square root in the denominator, multiply both the numerator and the denominator by $$ \sqrt{11} $$:

$$
   \frac{\sqrt{10}}{\sqrt{11}} \times \frac{\sqrt{11}}{\sqrt{11}} = \frac{\sqrt{10} \times \sqrt{11}}{11}
   $$

3. **Simplify the Numerator:**
   
   Multiply the radicals in the numerator:

$$
   \sqrt{10} \times \sqrt{11} = \sqrt{110}
   $$

4. **Final Simplified Form:**
   
   $$
   \frac{\sqrt{110}}{11}
   $$

So, the simplified form of $$ \sqrt{\frac{10}{11}} $$ is:

$$
\boxed{\dfrac{\sqrt{110}}{11}}
$$
$$ \sqrt{\frac{10}{11}} = \frac{\sqrt{110}}{11} $$

(Simplify your answer, including any radicals.

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