17. \( \frac{9 \sqrt{200}}{12 \sqrt{2}}= \)

To simplify \( \frac{9 \sqrt{200}}{12 \sqrt{2}} \), let's break it down step by step. First, simplify \( \sqrt{200} \): \(\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10 \sqrt{2}\). Now, substitute this back into the expression: \(\frac{9 \times 10 \sqrt{2}}{12 \sqrt{2}} = \frac{90 \sqrt{2}}{12 \sqrt{2}}\). The \( \sqrt{2} \) in the numerator and denominator will cancel out, leaving us with: \(\frac{90}{12}\). Now, simplifying \( \frac{90}{12} \): \(\frac{90 \div 6}{12 \div 6} = \frac{15}{2}\). So, \(\frac{9 \sqrt{200}}{12 \sqrt{2}} = \frac{15}{2}\) or \(7.5\).