Solve the Nested Radical Equation: √(16/∛64) = √(x²)

To solve the problem $\sqrt{\frac{16}{\sqrt[3]{64}}} = \sqrt{x^2}$, we proceed step-by-step as follows:

• First, we simplify $\sqrt[3]{64}$. Since $64 = 4^3$, it follows that $\sqrt[3]{64} = 4$.
• Next, simplify the expression $\frac{16}{\sqrt[3]{64}}$:
  $\frac{16}{4} = 4$.
• Now, take the square root of this simplified value. Thus, $\sqrt{4} = 2$.
• The equation simplifies to: $\sqrt{x^2} = 2$. Since $\sqrt{x^2} = |x|$, we have $|x| = 2$.
• This implies $x = 2$ or $x = -2$.
• However, choices include only positive solutions, and thus $x = 2$.

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