Question

Simplify cube root
^3√128

Answer 1

To simplify \(\sqrt[3]{128}\), we can first factor \(128\) into its prime factors.

The prime factorization of \(128\) is:
\[
128 = 2^7
\]

Now we can use the properties of cube roots:
\[
\sqrt[3]{128} = \sqrt[3]{2^7} = \sqrt[3]{(2^6) \cdot 2} = \sqrt[3]{2^6} \cdot \sqrt[3]{2}
\]

We know that:
\[
\sqrt[3]{2^6} = 2^{6/3} = 2^2 = 4
\]

So, we have:
\[
\sqrt[3]{128} = 4 \cdot \sqrt[3]{2}
\]

Thus, the simplified form of \(\sqrt[3]{128}\) is:
\[
\boxed{4\sqrt[3]{2}}
\]