Solve the Square Root Equation: x^6 = √16 · √25

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

• Step 1: Simplify $\sqrt{\sqrt{16}}$.
• Step 2: Simplify $\sqrt{25}$.
• Step 3: Calculate the right-hand side.
• Step 4: Solve $\sqrt{x^6} =$ computed right-hand side.

Now, let's work through each step:
Step 1: Simplify $\sqrt{\sqrt{16}}$.
We know that $\sqrt{16} = 4$, and $\sqrt{4} = 2$. So, $\sqrt{\sqrt{16}} = 2$.

Step 2: Simplify $\sqrt{25}$.
We know that $\sqrt{25} = 5$.

Step 3: Calculate the entire right-hand side.
We have $\sqrt{\sqrt{16}} \cdot \sqrt{25} = 2 \cdot 5 = 10$.

Step 4: Solve $\sqrt{x^6} = 10$.
Rewrite the left side as $(x^6)^{1/2} = x^{6/2} = x^3$.
Thus, $x^3 = 10$.

Therefore, the solution to the problem is $x^3 = 10$.