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Let's go through the problems one by one based on the image you uploaded:

### 1. Simplify the expressions:
#### a. \( 2 \sqrt[3]{5} + 3 \sqrt[3]{5} - \sqrt[3]{5} \)
- Combine like terms (cube roots of 5):
  \[
  (2 + 3 - 1) \sqrt[3]{5} = 4 \sqrt[3]{5}
  \]

#### b. \( 4 \sqrt{2} - \sqrt{18} + \frac{2}{5} \sqrt{50} \)
- Simplify each term:
  \[
  \sqrt{18} = \sqrt{9 \times 2} = 3 \sqrt{2}, \quad \sqrt{50} = \sqrt{25 \times 2} = 5 \sqrt{2}
  \]
  So, the expression becomes:
  \[
  4 \sqrt{2} - 3 \sqrt{2} + \frac{2}{5} \times 5 \sqrt{2} = 4 \sqrt{2} - 3 \sqrt{2} + 2 \sqrt{2}
  \]
  Combine like terms:
  \[
  (4 - 3 + 2) \sqrt{2} = 3 \sqrt{2}
  \]

### 2. Perform the multiplication of radicals:
#### a. \( 3 (2 \sqrt[3]{5}) \)
- Multiply the constants and keep the cube root:
  \[
  3 \times 2 \sqrt[3]{5} = 6 \sqrt[3]{5}
  \]

#### b. \( (4 \sqrt{2})(3 \sqrt{5}) \)
- Multiply the constants and the square roots separately:
  \[
  4 \times 3 = 12, \quad \sqrt{2} \times \sqrt{5} = \sqrt{10}
  \]
  So the result is:
  \[
  12 \sqrt{10}
  \]

### 3. Simplify the following division of radicals:
#### a. \( \frac{2 \sqrt{3}}{\sqrt{6}} \)
- Simplify the radical expression:
  \[
  \frac{2 \sqrt{3}}{\sqrt{6}} = \frac{2 \sqrt{3}}{\sqrt{2} \times \sqrt{3}} = \frac{2 \sqrt{3}}{\sqrt{6}} = 2 \sqrt{\frac{1}{2}} = 2 sqrt

Simplify radical expressions and perform operations on radicals (addition, multiplication, division) and logarithmic calculations.

This problem set covers simplifying radical expressions, performing addition, multiplication, division of radicals, and solving logarithmic equations. Suitable for students in Grades 10-12.

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