https://file.aiquickdraw.com/mathbot/file/17267706786048fckdhrb.jpg

The expression in the image is:

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

Let's break it down step by step:

1. **First term**: \(\sqrt{7^2 + 7^2}\)
   \[
   7^2 = 49
   \]
   \[
   7^2 + 7^2 = 49 + 49 = 98
   \]
   \[
   \sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2} \approx 9.899
   \]

2. **Second term**: \(4^3\)
   \[
   4^3 = 64
   \]

3. **Third term**: \(\sqrt[3]{81}\)
   \[
   81 = 3^4
   \]
   \[
   \sqrt[3]{81} = \sqrt[3]{3^4} = 3 \times \sqrt[3]{3} \approx 3 \times 1.442 = 4.326
   \]

So, putting it all together:

\[
7\sqrt{2} + 64 + 4.326 \approx 9.899 + 64 + 4.326 = 78.225
\]

The approximate value of the expression is **78.225**.

Would you like further details on this calculation, or do you have any questions?

Here are five related questions:
1. How would the expression change if \(4^3\) was replaced by \(5^3\)?
2. What would be the result if we replaced \(7^2\) with \(8^2\) in the first term?
3. How do you simplify square roots like \(\sqrt{98}\) more generally?
4. What is the value of \(\sqrt[4]{81}\) and how does it differ from the cube root?
5. Can you find the exact value of \(7\sqrt{2} + 4\sqrt[3]{3}\)?

**Tip:** When dealing with square roots or cube roots, factorization can simplify your calculations significantly!

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

Learn how to solve the expression √(7^2 + 7^2) + 4^3 + ∛81 with step-by-step calculations. This problem involves algebraic concepts, such as square roots, cube roots, and exponents. Suitable for students in Grades 8-10.

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