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.