Math Snap

STEP 1

1. We are given the expression $16 \sqrt[3]{3}$ and need to express it as a single radical.
2. The expression involves a cube root, so we will work with cube roots throughout the process.

STEP 2

1. Express the integer part as a cube root.
2. Combine the cube roots into a single radical expression.

STEP 3

Express the integer $16$ as a cube root. We know that:
$$16 = 2^4$$ To express $16$ as a cube root, we write:
$$16 = (2^4) = (2^3) \cdot 2 = \sqrt[3]{2^3} \cdot 2$$

STEP 4

Now, express $16$ as a cube root:
$$16 = \sqrt[3]{2^3 \cdot 2} = \sqrt[3]{2^4}$$

STEP 5

Combine the cube roots $\sqrt[3]{2^4}$ and $\sqrt[3]{3}$ into a single radical:
$$16 \sqrt[3]{3} = \sqrt[3]{2^4} \cdot \sqrt[3]{3}$$ Using the property of radicals, we can combine them:
$$= \sqrt[3]{2^4 \cdot 3}$$

Simplify the expression inside the cube root:
$$2^4 \cdot 3 = 16 \cdot 3 = 48$$ So, the entire radical expression is:
$$\sqrt[3]{48}$$ The expression $16 \sqrt[3]{3}$ as an entire radical is:
$$\boxed{\sqrt[3]{48}}$$