STEM REASONING AND EVIDENCE WORKBENCH
Extract complete square factors from positive integer radicands and audit fully simplified learner forms with exact evidence.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
Find the greatest perfect-square factor s squared that divides the positive integer n. Then square root n equals s times square root of n divided by s squared. The engine repeatedly extracts square factors until the remaining radicand has no square divisor greater than one, and separately checks whether the learner form still squares to the original value. Supported means the coefficient and remaining radicand match the fully simplified exact form. Equivalent but incomplete means the learner preserved the value but left another square factor inside. A value conflict means the entered form changes the radical. Review factorization evidence before assigning a misconception from one response.
Confirm the question, approved source, units, notation, signs, response coding, model assumptions, and review threshold. Keep an unchanged copy of measurements or learner evidence.
Run the worked example, inspect every intermediate row, and compare the result with a hand calculation, diagram, representation, periodic table, or approved laboratory method.
Record the method, assumptions, uncertainty, units, classifications, and flagged rows. Verify the editable report independently before instruction, assessment, or laboratory use.
How to interpret the result
Use after learners have practiced square factors and need evidence about incomplete extraction, changed values, or confusion between addition and multiplication. The diagnostic is deliberately bounded to principal square roots of positive integers. It does not simplify variables, fractions, cube roots, nested radicals, rationalized denominators, or complex values.
The square root of 72 becomes 6 square root 2 because 36 is its greatest square factor. Thirty is already square-free, and the square root of 196 becomes 14. For 180, the learner form 3 square root 20 preserves the value, but 20 still contains factor 4; the complete form is 6 square root 5.
Find the greatest perfect-square factor s squared that divides the positive integer n. Then square root n equals s times square root of n divided by s squared. The engine repeatedly extracts square factors until the remaining radicand has no square divisor greater than one, and separately checks whether the learner form still squares to the original value.
Supported means the coefficient and remaining radicand match the fully simplified exact form. Equivalent but incomplete means the learner preserved the value but left another square factor inside. A value conflict means the entered form changes the radical. Review factorization evidence before assigning a misconception from one response.
Do not split a radical across addition, divide the radicand without moving the square root of the factor outside, add the outside and inside numbers, leave a perfect-square factor hidden, or convert to a rounded decimal when exact form is required. Square the proposed form and use a factor tree or area model to verify.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish a chemical structure, or replace teacher, laboratory, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the school-approved system.
No. It describes entered evidence under one disclosed rule. Compare several evidence sources and ask for reasoning before drawing a conclusion.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow the course method and academic-integrity rules.
YOUR NIRMION
