Back to Solve rational and radical equations — Problem 3 · Task Set 33

HSA.REI.A.2 Tutor Intake — Rational and Radical Equations

This short check helps your tutor understand where to start. Answer each question without help. If you are not sure, give your best try — the goal is to find what to work on together, not to grade you.

Grade 9·8 problems·~13 min·Common Core Math - HS Algebra·standard·hsa-rei-a-2

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Concepts

Why can squaring both sides of a radical equation introduce an extraneous
solution?

Squaring always changes the solution set because it is not a legal
algebraic operation.

Squaring loses sign information: if $A = B$ then $A^2 = B^2$ , but
$A^2 = B^2$ only implies $|A| = |B|$ , not necessarily $A = B$ .

Squaring is only valid when both sides are positive, so any negative
solution is automatically extraneous.

Squaring introduces extraneous solutions because the radical's domain
is restricted to non-negative numbers.