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!