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

Annotations already declare readOnlyHint, idempotentHint, destructiveHint=false, and openWorldHint=false, so safety is covered. The description adds useful behavioral context beyond annotations: the operation is exact, uses integer factors, and accepts a bounded nonnegative integer domain.

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?

A single sentence with no wasted words, front-loading the operation, input domain, and output form. It is appropriately sized for a simple unary mathematical tool.

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?

Given the presence of an output schema, the description need not explain return values. For a one-parameter pure function with full schema coverage and safety annotations, the description contains everything needed to invoke the tool correctly.

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%, so the single parameter is already fully documented by the schema. The description restates the input domain ('integer from 0 to 10^12'), which is consistent with the schema but does not add new parameter-level meaning.

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?

States a specific verb ('Rewrite') and resource ('square root of an integer') with the exact output form 'a√b' and input domain '0 to 10^12'. This clearly distinguishes it from sibling math utilities such as power, logarithm, or quadratic_solve.

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 description explains what the tool does but gives no guidance on when to use it versus alternatives, nor any prerequisites or exclusions. Usage is only inferable from the name and mathematical operation.

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