Simplify the Nested Radical: √(16/∛64) Step-by-Step Solution

To solve this problem, we'll follow these steps:

• Step 1: Calculate the cube root of 64
• Step 2: Simplify the fraction $\frac{16}{\sqrt[3]{64}}$
• Step 3: Simplify $\sqrt{\text{result from step 2}}$

Let's proceed with each step:
Step 1: The cube root of 64 is calculated as follows:
$\sqrt[3]{64} = 4$. This is because $4^3 = 64$.

Step 2: Now, simplify the fraction $\frac{16}{4}$:
$\frac{16}{4} = 4$.

Step 3: Finally, take the square root of the result from step 2:
$\sqrt{4} = 2$.

Therefore, the solution to the problem is $2$.