Let's solve the problems from the uploaded image:

Problem 14: Simplify $\sqrt[3]{\frac{25}{27}}$

1. We rewrite the cube root as: [ \sqrt[3]{\frac{25}{27}} = \frac{\sqrt[3]{25}}{\sqrt[3]{27}} ]

2. Evaluate each term:

   • $\sqrt[3]{25}$ cannot be simplified further since 25 is not a perfect cube.
   • $\sqrt[3]{27} = 3$ (because $3^3 = 27$).

   So, the simplified form is: $\frac{\sqrt[3]{25}}{3}$

Problem 17: Simplify $\frac{3}{\sqrt{5}}$ with no radicals in the denominator

1. To rationalize the denominator, multiply numerator and denominator by $\sqrt{5}$: $\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{3\sqrt{5}}{5}$

   The simplified form is: $\frac{3\sqrt{5}}{5}$

Would you like a step-by-step breakdown for any of these problems?

Here are 5 related questions to expand your understanding:

1. How do you rationalize a denominator when it involves higher-order roots (e.g., cube roots)?
2. What are some common strategies for simplifying radicals?
3. How do you handle cube roots with variables in the numerator and denominator?
4. Why do we rationalize the denominator in mathematical expressions?
5. How can you simplify $\sqrt[3]{a^2b^5}$ for practice?

Tip:

Always ensure the denominator is free of radicals by multiplying by the appropriate conjugate or root factor to simplify properly.