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I see the mathematical expressions for simplification or rationalization of radicals in the uploaded image. Let's go through each item one by one:

### a. \(\sqrt{15x^3y^3z} + 5\sqrt{960xy^5z^3} + \sqrt{540x^5yz^5}\)
This involves simplifying each radical expression. We will first factor out any perfect squares (or cubes) from under the radicals to simplify them.

### b. \(\sqrt[4]{15} \cdot \sqrt[4]{\frac{1875}{540}}\)
This requires simplifying the expression by first dividing the terms inside the radicals and then simplifying the fourth roots.

### c. \(\sqrt[4]{3} \cdot \sqrt[5]{4}\)
We'll need to simplify this by rationalizing if possible or representing it in terms of exponents.

### d. \(\frac{155 + \sqrt{7}}{\sqrt{7}}\)
This is a rationalization problem. Multiply the numerator and denominator by \(\sqrt{7}\) to eliminate the square root in the denominator.

### e. \(\frac{\sqrt{7}}{155 + \sqrt{7}}\)
Again, rationalization by multiplying both the numerator and denominator by the conjugate of \(155 + \sqrt{7}\) will help simplify this.

### f. \(\frac{\sqrt{x}}{27 + \sqrt{x}}\)
Similar to (e), rationalize by multiplying by the conjugate of \(27 + \sqrt{x}\).

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Would you like me to proceed with the detailed solution for each part? Feel free to ask for any clarification. Here are five related questions you could consider:

1. What are the general steps for rationalizing a denominator involving radicals?
2. How do we simplify expressions involving fourth or fifth roots?
3. When multiplying radicals, what rules should be followed?
4. How can perfect squares and cubes inside a radical help in simplification?
5. What is the significance of the conjugate in rationalizing denominators?

**Tip:** Always check for perfect square or cube factors when simplifying radicals, as it makes the process smoother.

Simplify or rationalize the following radicals.

This exercise involves simplifying and rationalizing radicals, including square and fourth roots, and applying algebraic techniques such as using conjugates and identifying perfect square factors. Suitable for high school students studying algebra and radical expressions.

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