The given expression is:

\[
\sqrt[5]{96} + \sqrt[5]{3}
\]

We can rewrite it in terms of fractional exponents:

\[
96^{\frac{1}{5}} + 3^{\frac{1}{5}}
\]

Using a calculator, approximate the values of each term:

- \( 96^{\frac{1}{5}} \approx 2.7144 \)
- \( 3^{\frac{1}{5}} \approx 1.2457 \)

Now, summing these two values:

\[
2.7144 + 1.2457 \approx 3.9601
\]

Thus, the approximate value of the expression is:

\[
\boxed{3.9601}
\]

Would you like more details on how these roots were calculated or further questions? Here are some related questions:

1. How do you compute roots of higher degrees manually?
2. What is the significance of fractional exponents in mathematics?
3. Can this expression be simplified further without a calculator?
4. How do we handle complex numbers in roots of negative values?
5. How are roots of prime numbers handled in higher degrees?

**Tip**: Fractional exponents (like \(x^{1/n}\)) represent the nth root of a number, and they are often used in simplifying and solving root problems.

Learn how to solve the expression √[5]{96} + √[5]{3} using fractional exponents. This solution involves approximating the 5th roots of both numbers, simplifying with the formula x^(1/n), and summing the results. Suitable for Grades 10-12.

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