Grade 11Algebraic ThinkingOriginal practice

Rational Radical Equations and Valid Solutions: Explore and Explain Worksheet — Grade 11

Rational Radical Equations and Valid Solutions: Explore and Explain: Record domains before algebraic transformations. Starts with 2 practice tasks. Answer guidance included. Print on Letter/A4 or save as PDF from the print window.

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Independent activity · About 12 minutes · Pencil · Algebra 2

Practice set 1 of 3. Each set keeps the same learning goal and task structures.

Sheet 9B93265B · questions and answers share this ID

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Grade 11 · Mathematics

Rational Radical Equations and Valid Solutions: Explore and Explain

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Grade 11 · Mathematics · continued

Rational Radical Equations and Valid Solutions: Explore and Explain

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Equations before and after squaring

Work over real numbers. Consider √(x + 4) = x − 2. Squaring produces candidates, not automatically valid solutions. Also compare R(x) = (x² − 4)/(x − 2) with its simplified rule; its original denominator restriction remains.

Worked example: √(x + 1) = x − 1 gives x = 0 or 3 after squaring. Only 3 satisfies the original equation; 0 has a negative right side. Explore the material. Talk through your reasoning with suitable support.

1.What restriction follows because the square root must equal a nonnegative right side?

2.Square and rearrange the radical equation into a quadratic equal to zero.

Grade 11 · Mathematics · Answer key

Rational Radical Equations and Valid Solutions: Explore and Explain

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Open responses use criteria and an illustrative response. Other well-supported responses can be acceptable.

Grade 11 · Mathematics · Answer key · continued

Rational Radical Equations and Valid Solutions: Explore and Explain

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Equations before and after squaring

1.What restriction follows because the square root must equal a nonnegative right side?

Answer:x ≥ 2

2.Square and rearrange the radical equation into a quadratic equal to zero.

Answer:x² − 5x = 0

About this practice

Grade 11 · Mathematics · Matching answer key included · US Letter and A4

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Teaching guide, sample answers and curriculum references

Before you begin

Factor quadratics, solve linear equations and interpret principal square roots.

How to use this worksheet

Begin with: What restriction follows because the square root must equal a nonnegative right side?
Connect the response to: List all roots of that quadratic.
Ask students to apply the idea: Explain why squaring made x = 0 appear as a candidate although it fails the original equation.

A common mistake to discuss

An algebraic candidate is not a solution until it satisfies the original domain and equation.

What to practice next

Continue to Rational Radical Equations and Valid Solutions: Practice Independently.

Original instructional material written for this practice.

Source reference: Selected high-school course targets.

Published 2026-10-08; updated 2026-10-08. Read our editorial policy.

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Rational Radical Equations and Valid Solutions

Equations before and after squaring

Worked example: √(x + 1) = x − 1 gives x = 0 or 3 after squaring. Only 3 satisfies the original equation; 0 has a negative right side. Use the material to work through each task. Show the requested response.

1.What restriction follows because the square root must equal a nonnegative right side?

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions

Practice · Independent · 45 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Rational Radical Equations and Valid Solutions: Apply and Create

Equations before and after squaring

Use what you learned to explain, construct or apply an idea.

1.Explain why squaring made x = 0 appear as a candidate although it fails the original equation.

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions: Apply and Create

Apply · Independent · 25 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

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Rational Radical Equations and Valid Solutions: Practice Independently

Equations before and after squaring

Use the material to work through each task. Show the requested response.

1.List all roots of that quadratic.

Practice preview

Grade 11

Key

Rational Radical Equations and Valid Solutions: Practice Independently

Practice · Independent · 20 min

Record domains before algebraic transformations. Find candidates and check original equations. Explain extraneous roots and excluded inputs. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

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Practice preview

Grade 11

HSF.LE.A.4 Key

Algebra 2: Exponential & Logarithmic Functions

Practice · Independent · 35 min

Selected high-school practice with evidence, conditions and a written explanation.

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