STEM PRACTICE AND EVIDENCE WORKBENCH
Extract the largest perfect-square factor from positive integer radicands and audit learner outside and inside factors.
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
Search downward from the integer square root of n for the largest factor r such that r squared divides n. Set outside = r and inside = n divided by r squared. Then square root n = outside times square root inside. Because the largest square factor was extracted, inside has no remaining perfect-square factor greater than one. Supported means both learner factors match the canonical positive simplification. Equivalent-looking expressions should be checked by squaring or multiplying their radicands, but a nonmaximal extraction is not fully simplified. Connect the table with an area model, prime-factor pairs, perfect-square benchmarks, and estimation. Extend cautiously when negative values, variables, absolute value, domains, or complex numbers appear.
Confirm the learning question, authoritative source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence and remove learner names or identifiers.
Run the worked example first, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method. Correct input evidence before interpreting a flag.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently, connect the numerical signal with learner reasoning, and document any teaching or laboratory decision outside this tool.
How to interpret the result
Use when learners need a transparent bridge from square-factor decomposition to simplified radical notation. The evidence table exposes the largest square and remaining factor instead of returning only a final answer. It does not rationalize denominators, combine unlike radicals, solve radical equations, infer a factorization strategy from learner work, or apply absolute-value rules to variable expressions.
Twelve is 2 squared times 3, so its simplified form is 2 square root 3. Seventy-two is 6 squared times 2, and forty-nine is 7 squared times 1, becoming 7. Twenty is 2 squared times 5, so the loaded learner factors 4 and 5 reconstruct a different value and are flagged with the expected pair.
Search downward from the integer square root of n for the largest factor r such that r squared divides n. Set outside = r and inside = n divided by r squared. Then square root n = outside times square root inside. Because the largest square factor was extracted, inside has no remaining perfect-square factor greater than one.
Supported means both learner factors match the canonical positive simplification. Equivalent-looking expressions should be checked by squaring or multiplying their radicands, but a nonmaximal extraction is not fully simplified. Connect the table with an area model, prime-factor pairs, perfect-square benchmarks, and estimation. Extend cautiously when negative values, variables, absolute value, domains, or complex numbers appear.
Do not divide the radicand by a factor that is not squared, move a factor outside unchanged instead of taking its root, add inside and outside factors, call square root 49 equal to plus or minus 7, overlook a larger square factor, or turn square root 20 into 4 square root 5. Reconstruct the original radicand as outside squared times inside.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish assessment validity, or replace teacher, laboratory, curriculum, accessibility, 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 approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
