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

Annotations already cover readOnly/idempotent/destructive status, and the description adds genuinely useful context beyond them: leading-zero rejection, the 600-digit input bound, and the x402 micropayment requirement. It doesn't spell out the failure/return shape for non-squares, but the added constraints and payment model are valuable.

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?

Front-loaded with the core question, followed by a one-line example pair, then constraints and pricing. No wasted sentences; every clause carries information.

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?

No output schema exists, and the description adequately conveys the return (boolean plus the root when square) plus input constraints and the paid-call model. Nothing an agent needs to call it correctly 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?

With schema description coverage at 0%, the description compensates well: it defines the parameter domain (non-negative integer), rejects leading zeros, and caps length at 600 digits, matching the schema pattern. It doesn't restate that n is passed as a string, leaving a small gap.

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 operation ('whether a non-negative decimal integer is a perfect square, and the root when it is') with clarifying examples (16→4, 15→not). This is clearly distinct from sibling isqrt in that it returns a boolean plus conditional root, though it never names isqrt or perfect_check to make the contrast explicit.

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?

The examples and the 'perfect square' framing imply when to use it, but there is no explicit when-to-use vs when-not guidance against close alternatives like isqrt or squarefree. An agent must infer the routing itself.

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