Write the following in simplified radical form \( \sqrt[4]{96} \)

To simplify \( \sqrt[4]{96} \), we start by breaking down 96 into its prime factors: \( 96 = 16 \times 6 = 2^4 \times 6 = 2^4 \times 2 \times 3 = 2^5 \times 3 \). Now, we can write this as \( \sqrt[4]{2^5 \times 3} \). According to the properties of radicals, this can be separated into two parts: \[ \sqrt[4]{2^4} \times \sqrt[4]{2} \times \sqrt[4]{3} \] Simplifying \( \sqrt[4]{2^4} \) gives us \( 2 \), so we have: \[ 2 \times \sqrt[4]{2 \times 3} = 2 \times \sqrt[4]{6 \sqrt{6}} \] Thus, the simplified radical form of \( \sqrt[4]{96} \) is: \[ 2 \sqrt[4]{6} \]