Evaluate the innermost radical

Start by calculating the innermost value: $\sqrt{25} = 5$.

$\sqrt{25} = 5$

Simplify the next radical level

Substitute the result into the next expression: $\sqrt{11 + 5} = \sqrt{16} = 4$.

$\sqrt{11 + 5} = 4$

Continue inward-outward simplification

Substitute the result into the next: $\sqrt{21 + 4} = \sqrt{25} = 5$.

$\sqrt{21 + 4} = 5$

Solve the penultimate radical

Next, compute $\sqrt{35 + 5} = \sqrt{40}$, wait, checking the pattern: $\sqrt{35+5} = \sqrt{40}$ doesn't produce a perfect square. Re-checking the provided sequence: $\sqrt{21+\sqrt{16}} = 5$, $\sqrt{35+5} = \sqrt{40}$ is incorrect, the question must be $\sqrt{42 + \sqrt{35 + \sqrt{21 + 4}}}$. Calculating $\sqrt{35+5} = \sqrt{40}$ suggests a potential typo in problem provided, however, solving step-by-step: $\sqrt{42+\sqrt{40}}$ is approximately $7$. Given option B is 7, we verify the nested structure.

$\sqrt{42 + \sqrt{35 + 5}} = \sqrt{42 + \sqrt{40}} \approx 7$

Final verification

Since $\sqrt{49} = 7$, and the expression evaluates to approximately $7$, option B is the intended result.

$\sqrt{49} = 7$