sqrt2

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

No annotations are provided, so the description carries the full burden. It states the tool returns a specific approximation ('≈ 1.41421'), which is useful behavioral context about precision. However, it doesn't mention whether this is a read-only operation, if it has side effects, or any error conditions. For a zero-parameter tool, this is minimally adequate but lacks depth.

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 description is extremely concise and front-loaded: the first sentence ('Get √2 ≈ 1.41421.') directly states the tool's core function. The second sentence adds historical/mathematical context, and the parenthetical provides domain categorization. Every sentence earns its place with no wasted words.

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?

For a zero-parameter tool with no output schema and no annotations, the description is reasonably complete. It specifies what the tool returns (√2 approximation) and provides mathematical context. However, it doesn't detail the exact return format (e.g., numeric type, precision) or potential errors, which could be helpful for an agent. Given the simplicity, it's mostly adequate.

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?

The tool has zero parameters, and the input schema has 100% description coverage (empty object). The description doesn't need to explain parameters, and it doesn't. It correctly focuses on the tool's output. With no parameters, the baseline is 4, as there's nothing to compensate for.

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 clearly states the tool's purpose: 'Get √2 ≈ 1.41421. Square root of 2, first known irrational number.' It specifies the exact verb ('Get') and resource (the mathematical constant √2), and distinguishes it from siblings like sqrt, sqrt3, sqrt5 by focusing specifically on √2. The domain/category context further clarifies its mathematical nature.

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 implies usage through its mathematical context ('Domain: arithmetic, Category: general'), suggesting it's for arithmetic calculations involving √2. However, it doesn't explicitly state when to use this tool versus alternatives like sqrt (which calculates square roots generally) or other constant tools (like pi, e). The guidance is implied rather than explicit.

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