Rationalize the denominator. If possible, simplify the rationalized expression by dividing the numerator and denominator by the greatest common factor. \( \frac{1}{\sqrt{10}} \) \( \frac{1}{\sqrt{10}}=\square \) (Type a simplified fraction. Simplify your answer.)

To rationalize the denominator of \( \frac{1}{\sqrt{10}} \), we can multiply the numerator and denominator by \( \sqrt{10} \). This gives us: \[ \frac{1 \cdot \sqrt{10}}{\sqrt{10} \cdot \sqrt{10}} = \frac{\sqrt{10}}{10} \] So, \( \frac{1}{\sqrt{10}} = \frac{\sqrt{10}}{10} \). To double-check, we realize there are no common factors between \( \sqrt{10} \) and \( 10 \), thus this is already in its simplest form. Therefore: \[ \frac{1}{\sqrt{10}} = \frac{\sqrt{10}}{10} \]