To simplify [tex]\(\sqrt[3]{56}\)[/tex], let's first break down the number 56 into its prime factors:
1. We start by finding the prime factorization of 56:
[tex]\[
56 = 2 \times 28
\][/tex]
Next, we factorize 28:
[tex]\[
28 = 2 \times 14
\][/tex]
Finally, we factorize 14:
[tex]\[
14 = 2 \times 7
\][/tex]
Putting it all together, we have:
[tex]\[
56 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7
\][/tex]
2. Now considering the cube root of 56, we can express it as:
[tex]\[
\sqrt[3]{56} = \sqrt[3]{2^3 \times 7}
\][/tex]
3. Applying the property of cube roots that allows us to separate factors, we get:
[tex]\[
\sqrt[3]{2^3 \times 7} = \sqrt[3]{2^3} \times \sqrt[3]{7}
\][/tex]
4. Since [tex]\( \sqrt[3]{2^3} = 2 \)[/tex], this simplifies further to:
[tex]\[
\sqrt[3]{2^3} \times \sqrt[3]{7} = 2 \times \sqrt[3]{7}
\][/tex]
Thus, the simplified form of [tex]\(\sqrt[3]{56}\)[/tex] is:
[tex]\[
2 \sqrt[3]{7}
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{2 \sqrt[3]{7}}
\][/tex]
