Solving Quadratics by Square Roots
I can solve a quadratic by taking square roots, keeping both signs.
The problem this sheet solves
The error here is incompleteness rather than a wrong value, which is why marking it wrong teaches nothing. Squaring throws the sign away, so undoing it has to put both signs back. A second fault outlives the first: after students learn the plus or minus they still stop at x minus 3 = plus or minus 4, which is not an answer — there is an equation left to solve, twice. The argument is one multiplication, not a rule about notation: ask what negative 5 times negative 5 is, and a student who answers 25 has just proved the second solution exists. The sheet names the connection to absolute value equations and reuses the same number-line figure on purpose, so the shared idea — an operation that discards the sign — is taught once rather than twice.
The key rule
Take the square root of both sides and write ±. Squaring throws the sign away, so undoing it has to put both signs back.
Two answers, not one.
Watch out
The mistake: For x2 = 25 a student answers x = 5.
The fix: 5 is right, and so is −5. Ask what (−5)(−5) is: 25. Squaring throws the sign away, so undoing it must give both.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.