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It looks like you've uploaded an image related to math questions. Let's analyze and solve the two questions shown in the image.

### **Question 1:**

**Use the product rule to simplify the expression.**
\[
\sqrt{5} \times \sqrt{11}
\]
Using the product rule for square roots:
\[
\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
\]
Apply this rule:
\[
\sqrt{5} \times \sqrt{11} = \sqrt{5 \times 11} = \sqrt{55}
\]

So, the simplified expression is **\(\sqrt{55}\)**.

### **Question 2:**

**Use the quotient rule to simplify the expression.**
\[
\frac{\sqrt{15}}{3}
\]
The quotient rule for square roots states:
\[
\frac{\sqrt{a}}{b} = \frac{\sqrt{a}}{b}, \quad \text{if } b \text{ is a non-zero number.}
\]
In this case:
\[
\frac{\sqrt{15}}{3}
\]
This expression is already simplified, so the answer is **\(\frac{\sqrt{15}}{3}\)**.

The answer selected (option \( \frac{\sqrt{15}}{3} \)) is correct.

---

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### Relative Questions:
1. What is the product rule for square roots, and how does it apply to variables?
2. How can the quotient rule be applied to expressions with variables under the square root?
3. Can the product rule be applied to cube roots in the same way?
4. What happens when you apply the product rule to two different radicals of higher degrees, e.g., \(\sqrt[3]{a} \times \sqrt[4]{b}\)?
5. How would you simplify an expression like \(\frac{\sqrt{20}}{5}\)?

### Tip:
Always check whether the numbers inside the square roots can be simplified further (e.g., perfect squares), as that might lead to a more reduced form.

Question 1: Use the product rule to simplify the expression: sqrt(5) × sqrt(11). Question 2: Use the quotient rule to simplify the expression: sqrt(15) / 3.

Learn how to simplify radical expressions using the product and quotient rules. This step-by-step guide walks you through simplifying sqrt(5) × sqrt(11) and sqrt(15) / 3, with detailed explanations of the formulas used. Ideal for students in Grades 8-10.

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