The question shown in the image asks for the result of the expression:

$12 \cdot 5^{\frac{1}{3}} + 6 \cdot 4^{\frac{1}{3}} - \sqrt{169}$

Let's break this down step by step:

1. First term: $5^{\frac{1}{3}}$ is the cube root of 5.

   • $5^{\frac{1}{3}} \approx 1.710$
   • Multiply by 12: $12 \cdot 1.710 \approx 20.52$.

2. Second term: $4^{\frac{1}{3}}$ is the cube root of 4.

   • $4^{\frac{1}{3}} \approx 1.587$
   • Multiply by 6: $6 \cdot 1.587 \approx 9.52$.

3. Third term: $\sqrt{169}$ is the square root of 169.

   • $\sqrt{169} = 13$.

Now, putting all of this together:

$20.52 + 9.52 - 13 = 17.04$

Final answer:

The value is approximately 17.04, but none of the options match exactly. The closest approximation is 22.

Would you like more details on any part of the calculation?

Here are 5 related questions:

1. What is the cube root of other numbers, like 8 or 27?
2. How do you calculate cube roots without a calculator?
3. Why is $\sqrt{169}$ equal to 13?
4. What other methods can be used to approximate cube roots?
5. How can we simplify this expression further for better accuracy?

Tip: Cube roots can be approximated using series expansion or logarithmic properties for more precise calculations.