The given expression in the image is:

$\sqrt{72^2 + 7^2} + 4^3 + \sqrt[3]{81}$

Let's break this down step by step:

1. Evaluate $72^2 + 7^2$: $72^2 = 5184, \quad 7^2 = 49$ So, $72^2 + 7^2 = 5184 + 49 = 5233$

2. Now, find $\sqrt{5233}$: $\sqrt{5233} \approx 72.33$

3. Evaluate $4^3$: $4^3 = 4 \times 4 \times 4 = 64$

4. Find $\sqrt[3]{81}$: The cube root of 81 is approximately: $\sqrt[3]{81} \approx 4.33$

5. Now, add all the terms: $\sqrt{5233} + 64 + \sqrt[3]{81} \approx 72.33 + 64 + 4.33 = 140.66$

So, the final result is approximately 140.66.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:

1. What is the general method for calculating square roots and cube roots of large numbers?
2. How does the Pythagorean theorem relate to expressions like $\sqrt{72^2 + 7^2}$?
3. Can the cube root of 81 be simplified using prime factorization?
4. What are the common uses of cube roots in real-world applications?
5. How do exponents affect calculations in different bases?

Tip: When working with roots and powers, estimating large values by approximation methods can save time in exams or quick calculations!