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

Annotations already declare readOnlyHint=true, destructiveHint=false and openWorldHint=false, so safety is fully covered and the description carries little extra burden. The worked examples (√25=5, ∛27=3, 4th root of 16=2) confirm deterministic real-valued output, but the description is silent on edge behavior such as negative radicands, zero, or non-integer roots, which is the one behavioral question an agent would actually have.

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?

Two short sentences, the usage instruction first and the illustrative examples second. Nothing is wasted and nothing is buried.

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?

With an output schema present and full parameter coverage, the description needn't explain return values, and it is adequate for correct invocation. The remaining gap is domain edge-case handling (negative values under even roots, n=0), which matters for a math tool but is a minor omission given the rich structured metadata.

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% and the n parameter already documents its conditional use with root_type=nth, so the schema does the heavy lifting and the baseline of 3 applies. The examples weakly reinforce the notation-to-parameter mapping but add no syntax or constraint detail beyond what the schema states.

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 names a specific operation and covers its three variants (square, cube, nth root) in a single clear sentence, so the agent knows exactly what it computes. It does not, however, differentiate itself from the similarly named sibling calculator_root_finder, which an agent could easily confuse with nth-root extraction.

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?

"Use this for square root, cube root, or nth root" gives an explicit triggering context rather than leaving usage implied. It stops short of any exclusion or alternative routing — notably it never says when to prefer calculator_root_finder or calculator_complex instead.

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