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I see you've uploaded a set of exercises on "Surds and other radicals." Let's work through a couple of these problems step by step.

### Problem 1:
**How many of the numbers \( \sqrt{1}, \sqrt{2}, \sqrt{3}, \ldots, \sqrt{100} \) are surds?**

- **Surd Definition**: A surd is an irrational root. Therefore, any square root of a number that is not a perfect square will be a surd.

- **Perfect squares between 1 and 100** are: \( 1^2 = 1 \), \( 2^2 = 4 \), \( 3^2 = 9 \), \( 4^2 = 16 \), \( 5^2 = 25 \), \( 6^2 = 36 \), \( 7^2 = 49 \), \( 8^2 = 64 \), \( 9^2 = 81 \), and \( 10^2 = 100 \).

- **Non-surds** (perfect squares) are \( \sqrt{1}, \sqrt{4}, \sqrt{9}, \sqrt{16}, \sqrt{25}, \sqrt{36}, \sqrt{49}, \sqrt{64}, \sqrt{81}, \sqrt{100} \).

Thus, there are 10 numbers that are not surds, and since there are 100 numbers in total, **90 numbers** are surds.

### Problem 2:
**Evaluate:**
\( \left( 5\sqrt{2} \right)^2 \)

- First, square both the constant and the surd:
  \[
  \left( 5\sqrt{2} \right)^2 = 5^2 \times \left( \sqrt{2} \right)^2 = 25 \times 2 = 50
  \]

Thus, \( \left( 5\sqrt{2} \right)^2 = 50 \).

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Would you like to continue solving more problems from this set? Let me know if you'd like detailed steps for any specific questions or explanations on certain concepts!

### 5 Related Questions:
1. What is a rational number and how does it differ from an irrational number?
2. How can you simplify expressions with surds?
3. Can a surd ever become a rational number after arithmetic operations?
4. What is the process for rationalizing the denominator in expressions with surds?
5. How do you determine if a square root is a surd without using a calculator?

**Tip:** When simplifying surds, always look for perfect square factors to help break down the square root more easily.

Solve the set of exercises on surds and other radicals from Review set 3B.

Solve exercises related to surds and radicals from Review set 3B. Learn key concepts like simplifying radicals, rationalizing denominators, and more. Suitable for students in Grades 8-10.

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