Math Snap

STEP 1

1. An entire radical is a radical expression that cannot be simplified further into a simpler radical form.
2. We need to determine which of the given numbers is not an entire radical.

STEP 2

1. Simplify each radical expression.
2. Identify the expression that is not an entire radical.

STEP 3

Simplify $\sqrt[3]{343}$.
Since $343 = 7^3$, we have:
$$\sqrt[3]{343} = \sqrt[3]{7^3} = 7$$

STEP 4

Simplify $\sqrt{16}$.
Since $16 = 4^2$, we have:
$$\sqrt{16} = \sqrt{4^2} = 4$$

STEP 5

Simplify $\sqrt{35}$.
The number $35$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $5$ and $7$.
$$\sqrt{35} \text{ remains as } \sqrt{35}$$

STEP 6

Simplify $3 \sqrt{42}$.
The number $42$ is not a perfect square, and it cannot be simplified further because it is the product of prime numbers $2$, $3$, and $7$.
$$3 \sqrt{42} \text{ remains as } 3 \sqrt{42}$$

Identify the expression that is not an entire radical.
The expressions $\sqrt[3]{343}$ and $\sqrt{16}$ simplify to whole numbers $7$ and $4$, respectively. The expressions $\sqrt{35}$ and $3 \sqrt{42}$ do not simplify to whole numbers, but $\sqrt{35}$ is a single radical expression that cannot be simplified further, making it an entire radical.
Therefore, the expression that is not an entire radical is:
$$\boxed{3 \sqrt{42}}$$