(sqrt (12))/(sqrt (10))cdot (sqrt (10))/(sqrt (10))

To simplify the expression \(\frac{\sqrt{12}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}\), we can follow these steps:<br /><br />1. Simplify the fraction \(\frac{\sqrt{12}}{\sqrt{10}}\):<br /> \[<br /> \frac{\sqrt{12}}{\sqrt{10}} = \sqrt{\frac{12}{10}} = \sqrt{\frac{6}{5}}<br /> \]<br /><br />2. Multiply the simplified fraction by \(\frac{\sqrt{10}}{\sqrt{10}}\):<br /> \[<br /> \sqrt{\frac{6}{5}} \cdot \frac{\sqrt{10}}{\sqrt{10}}<br /> \]<br /><br />3. Since \(\frac{\sqrt{10}}{\sqrt{10}} = 1\), the expression simplifies to:<br /> \[<br /> \sqrt{\frac{6}{5}}<br /> \]<br /><br />4. Finally, we can express \(\sqrt{\frac{6}{5}}\) as:<br /> \[<br /> \sqrt{\frac{6}{5}} = \frac{\sqrt{6}}{\sqrt{5}} = \frac{\sqrt{6}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{30}}{5}<br /> \]<br /><br />So, the simplified form of the given expression is:<br />\[<br />\frac{\sqrt{30}}{5}<br />\]