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

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: \[ \boxed{\dfrac{\sqrt{110}}{11}} \]