Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnly, idempotent, and closed-world, so the safety profile is covered. The description adds genuinely useful behavioral detail the annotations do not carry: output precision (10 decimal places), the additional simplest-radical-form result, and a squares-back verification. The only fault is that the trailing URL is promotional rather than behavioral.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The example is a strong, front-loaded demonstration of input and output, but the marketing web-page URL in the final clause consumes space without helping invocation. Overall a short description, though one of its two sentences does not earn its place.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

There is no output schema, so the description correctly carries the return-value burden, explaining the decimal result, radical form, and self-check. Parameters are fully schema-documented. For a two-parameter pure calculator with full annotations, this is essentially complete; only sibling routing is missing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100% – both n (root index) and x (number) are documented in the schema, including defaults, bounds, and the meaning of n=2/3. The description's 'square, cube or any nth root' merely restates the semantics already in the n parameter description, so the baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description states a specific verb+resource: compute square, cube, or any nth root, returning a decimal to 10 places plus simplest radical form. A leading worked example (√72 → 6√2 ≈ 8.4852813742) makes the output concrete. It does not, however, distinguish itself from the nearest sibling, exponent_calculator, which is the obvious alternative for the same underlying operation.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Implied usage is clear from 'Get square, cube or any nth root,' and the worked example shows the intended input shape. But there is no explicit when-to-use/when-not-to-use guidance and no routing to alternatives such as exponent_calculator or scientific_calculator, leaving the agent to infer selection.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.