https://file.aiquickdraw.com/mathbot/file/1726770325916pukzhc7l.jpg

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!

Simplify the expression: √(72^2 + 7^2) + 4^3 + ∛81

Learn how to simplify the expression √(72^2 + 7^2) + 4^3 + ∛81 with a detailed step-by-step solution. This problem covers key algebraic concepts such as square roots, cube roots, and exponentiation. Suitable for students in Grades 9-12.

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