calc.engineer

square root

square_root

Compute the square root of a non-negative number. Returns the decimal result, whether the input is a perfect square, and a simplified radical form (e.g. '√12' simplifies to '2√3'). For integer inputs, factors are extracted from under the radical sign. Useful for geometry (diagonal/hypotenuse calculations), statistics (standard deviation from variance), signal processing (RMS values), and general algebra. Chain with pythagorean_theorem for triangle side calculations.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`value`	Yes	The non-negative number to compute the square root of

Output Schema

TableJSON Schema

Name	Required	Description
`result`	Yes	The square root of the input value
`is_perfect_square`	Yes	True if the input is a perfect square integer
`simplified_radical`	Yes	Simplified radical form (e.g. '2√3' for √12)

TDQS

A4.3/5.0

Behavior4/5

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

Given no annotations, the description fully discloses key behaviors: returns decimal result, perfect square detection, simplified radical form, and integer factoring. It does not mention precision or handling of non-integer inputs for radical form, but overall is informative.

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

Conciseness5/5

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

The description is very concise comprising the core action in the first sentence, output details in the second, and usage examples in subsequent short sentences. No redundancy, every sentence adds value.

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

Completeness5/5

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

For a simple tool with one parameter and an output schema, the description covers all necessary aspects: what it does, output details, use cases, and cross-reference to a related tool. It is complete without being verbose.

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

Parameters3/5

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

Schema coverage is 100% with a clear description for the single parameter. The tool description adds no additional semantics beyond what the schema already provides, so baseline score of 3 is appropriate.

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

Purpose5/5

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

The description clearly states the tool computes the square root of a non-negative number, names the output components (decimal, perfect square flag, simplified radical form), and distinguishes from sibling tools like exponent_calc by focusing on square root specifically.

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

Usage Guidelines4/5

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

The description provides explicit usage contexts (geometry, statistics, signal processing, algebra) and suggests chaining with pythagorean_theorem, but does not mention when not to use this tool or compare to alternatives like exponent_calc or log_calc.

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

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TDQS

A3.9/5.0

Disambiguation4/5

Despite 89 tools, each has a clearly distinct purpose with detailed descriptions that often reference related tools. Overlap exists (e.g., multiple LoRa/RF tools), but the descriptions are sufficient to distinguish them. Some confusion possible among similar-sounding tools like attenuator_pi and attenuator_tee, but the descriptions explicitly compare them.

Naming Consistency4/5

Consistent underscore-separated lowercase naming. Most tools follow a verb_noun pattern (e.g., capacitor_charge, wire_gauge) or noun_noun (power_cost). Minor inconsistencies such as 'bmi_calculator' vs 'solar_sizing' but overall predictable.

Tool Count2/5

89 tools is far too many for a single MCP server. This scope is more appropriate for multiple specialized servers. The sheer number will slow agent selection and increase cognitive load, reducing coherence.

Completeness3/5

Covers many domains (RF, solar, PCB, networking, math, etc.) but lacks depth in some areas (e.g., no three-phase power, no airflow calculations). Some domains have comprehensive coverage (LoRa/Meshtastic), but others feel incomplete for the tool count.

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