Objective 1.2
Anatomy and Meaning of Radical Expressions
Build the language of radicals before converting, graphing, or simplifying them.
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Every lesson starts with meaning and prerequisites.Visible mathematics
Live models connect notation, structure, and graphs.Genuine practice
Predict first, receive targeted feedback, and revise.Mastery evidence
Save a learner reasoning record after completing each topic.1.2
Radical notation and rational exponents
5 focused lessons
Objective 1.2
Perfect Powers and Real nth Roots
Recognize perfect powers and decide when an nth root is real.
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Convert Between Radicals and Rational Exponents
Translate root notation into exponent notation and back without changing the value.
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Interpret Numerators and Denominators in Rational Exponents
Read a^(m/n) as both a root and a power.
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Evaluate Rational Exponents
Evaluate exact rational powers by choosing an efficient root–power order.
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Rules of rational exponents
3 focused lessons
Objective 1.3
Product and Quotient Rules with Rational Exponents
Multiply and divide powers with the same base using rational exponents.
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Power Rules with Rational Exponents
Apply powers to powers, products, and quotients.
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Zero and Negative Rational Exponents
Interpret zero and negative rational exponents before combining rules.
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Graph radical functions
6 focused lessons
Objective 1.1
Square-Root Parent Function
Build the graph of y = √x from its domain and exact anchor points.
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Transform Square-Root Functions
Graph y = a√(x − h) + k by transforming the parent graph.
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Domain, Range, and Intercepts of Square-Root Graphs
Read key graph features directly from radical function structure.
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Cube-Root Parent Function
Build y = ∛x from perfect cubes and distinguish it from y = √x.
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Transform Cube-Root Functions
Graph y = a∛(x − h) + k using its center and transformed anchors.
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Graph Other Radical Functions and Choose a Model
Extend graphing patterns to fourth roots, fifth roots, and other indices.
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Simplify radical expressions
5 focused lessons
Objective 1.4
Simplify Numerical Square Roots
Extract perfect-square factors so no square factor remains inside the radical.
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Simplify Variable Square Roots
Extract even powers correctly and use absolute value when required.
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Simplify Higher-Index Radicals
Extract perfect cubes, fourth powers, and other nth powers.
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Rationalize Monomial Denominators
Remove a radical from a one-term denominator using a form of 1.
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Rationalize Binomial Denominators with Conjugates
Use conjugates to eliminate radicals from two-term denominators.
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Add and subtract radicals
2 focused lessons
Objective 1.5
Add and Subtract Like Radical Expressions
Combine only radical terms with matching indices and radicands.
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Simplify Before Adding or Subtracting Radicals
Reveal hidden like radicals by simplifying every term first.
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