To simplify the expression \( 7\sqrt{2535} \), we need to find the simplest radical form of \( \sqrt{2535} \).

### Steps to simplify \( \sqrt{2535} \):

1. **Factorize 2535:**

   \[
   2535 \div 5 = 507
   \]
   \[
   507 \div 3 = 169
   \]
   \[
   169 = 13 \times 13
   \]

   So, the prime factorization of 2535 is:
   \[
   2535 = 5 \times 3 \times 13 \times 13
   \]

2. **Group the prime factors into pairs:**

   \( 2535 \) can be written as:
   \[
   2535 = 13^2 \times 5 \times 3
   \]

3. **Take the square root:**

   \[
   \sqrt{2535} = \sqrt{13^2 \times 5 \times 3} = 13 \times \sqrt{15}
   \]

   So, \( \sqrt{2535} = 13\sqrt{15} \).

4. **Multiply by 7:**

   \[
   7\sqrt{2535} = 7 \times 13\sqrt{15} = 91\sqrt{15}
   \]

Thus, the simplified form of \( 7\sqrt{2535} \) is \( 91\sqrt{15} \).

Would you like more details on this process or have other questions?

Here are five related questions:
1. How do you identify and extract square factors from a number under the square root?
2. What are common mistakes when simplifying square roots?
3. How can you simplify radical expressions involving variables?
4. What is the difference between simplifying a square root and rationalizing the denominator?
5. How do you handle square roots in algebraic expressions?

**Tip:** Always look for perfect square factors when simplifying a radical to ensure it is in its simplest form.

Learn how to simplify \( 7\sqrt{2535} \) using radical and prime factorization methods. Follow a step-by-step guide to simplify radical expressions and understand prime factorization. Suitable for high school students.

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