11) \( \frac{5 \sqrt{20}}{2 \sqrt{15}} \)

To simplify \( \frac{5 \sqrt{20}}{2 \sqrt{15}} \), start by simplifying the square roots in both the numerator and denominator. Since \( \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} \), we can rewrite the expression as \( \frac{5 \cdot 2 \sqrt{5}}{2 \sqrt{15}} \). This simplifies to \( \frac{10 \sqrt{5}}{2 \sqrt{15}} \). Dividing the numerator and denominator by 2 gives us \( \frac{5 \sqrt{5}}{\sqrt{15}} \). Next, simplify \( \sqrt{15} \) to \( \sqrt{3 \times 5} = \sqrt{3} \sqrt{5} \). Thus, we now have \( \frac{5 \sqrt{5}}{\sqrt{3} \sqrt{5}} \). The \( \sqrt{5} \) in the numerator and denominator cancels out, leaving us with \( \frac{5}{\sqrt{3}} \). To rationalize the denominator, multiply numerator and denominator by \( \sqrt{3} \), resulting in \( \frac{5 \sqrt{3}}{3} \). So, the simplified form is \( \frac{5 \sqrt{3}}{3} \).