Interpret the radical correctly and solve: If √(10 + ∛x) = 4, find the value of x.

Introduction / Context:
This problem mixes a square root and a cube root. Correctly interpreting the placement of the radical (over the binomial 10 + ∛x) is essential. After isolating the cube root by squaring, the result is a simple perfect cube.

Given Data / Assumptions:

• √(10 + ∛x) = 4 (principal square root, so both sides nonnegative).

Concept / Approach:
Square both sides to remove the square root, then isolate ∛x and finally cube both sides to solve for x. Check the solution in the original equation to avoid extraneous roots introduced by squaring.

Step-by-Step Solution:

Verification / Alternative check:
Substitute back: √(10 + ∛216) = √(10 + 6) = √16 = 4. Satisfied.

Why Other Options Are Wrong:

• 150, 316, 450: These do not yield ∛x = 6, and plugging them back fails the original equation.

Common Pitfalls:
Misreading the radical as √10 + ∛x (which would lead to a non-integer result), or forgetting to verify after squaring.

Final Answer: