Rationalize the denominator. \[ \frac{\sqrt{7}}{\sqrt{10}} \]

To **rationalize the denominator** of the expression \[ \frac{\sqrt{7}}{\sqrt{10}}, \] you need to eliminate the square root from the denominator. This can be achieved by multiplying both the numerator and the denominator by \(\sqrt{10}\). Here's a step-by-step breakdown: 1. **Multiply Numerator and Denominator by \(\sqrt{10}\):** \[ \frac{\sqrt{7}}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{\sqrt{7} \times \sqrt{10}}{\sqrt{10} \times \sqrt{10}} \] 2. **Simplify the Numerator and Denominator:** - **Numerator:** \(\sqrt{7} \times \sqrt{10} = \sqrt{7 \times 10} = \sqrt{70}\) - **Denominator:** \(\sqrt{10} \times \sqrt{10} = \sqrt{10^2} = 10\) So, the expression becomes: \[ \frac{\sqrt{70}}{10} \] 3. **Final Answer:** \[ \boxed{\dfrac{\sqrt{70}}{10}} \] This is the rationalized form of the original expression, with the denominator free of any square roots.